Works (144)

Updated: April 4th, 2024 03:31

2024 article

On the enumeration of subcells within hypercubes and its application to the Borsuk-Ulam theorem

Chu, M. T., & Lin, M. M. (2024, January 6). NUMERICAL ALGORITHMS, Vol. 1.

By: M. Chu n & M. Lin*

author keywords: Borsuk-Ulam theorem; Hypercubes; Generic coordinates; Homeomorphism; Spherical mean
Sources: Web Of Science, ORCID
Added: January 29, 2024

2023 journal article

An Innate Moving Frame on Parametric Surfaces: The Dynamics of Principal Singular Curves

Mathematics, 11(15), 3306.

By: M. Chu n & Z. Zhang*

author keywords: moving frame; nonlinear variation; gradient adaption; singular curves; critical curves; base pairings; parametric surfaces; geometric genome
Sources: ORCID, Web Of Science, Crossref
Added: July 29, 2023

2023 journal article

Lax dynamics for Cartan decomposition with applications to Hamiltonian simulation

IMA Journal of Numerical Analysis, 4, drad018.

By: M. Chu n

author keywords: Hamiltonian simulation; Cartan decomposition; Lax dynamics; exponential map
TL;DR: This paper aims at establishing the theoretic and algorithmic foundations by exploiting the geometric properties of Hamiltonian subalgebras and describing a common mechanism for deriving the Lax dynamics, and giving rise to a genuine unitary synthesis that not only is numerically feasible, but also can be utilized to gauge the quality of results produced by other means, and extend the knowledge to a wide range of applications. (via Semantic Scholar)
Sources: Web Of Science, ORCID, Crossref
Added: May 9, 2023

2022 journal article

A complex-valued gradient flow for the entangled bipartite low rank approximation

COMPUTER PHYSICS COMMUNICATIONS, 271.

By: M. Chu n & M. Lin*

Contributors: M. Chu n & M. Lin*

author keywords: Quantum states; Entanglement; Separability; Bipartite system; Low-rank approximation; Gradient dynamics; Wirtinger calculus
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID
Added: March 7, 2022

2022 journal article

Low-rank approximation to entangled multipartite quantum systems

QUANTUM INFORMATION PROCESSING, 21(4).

By: M. Lin* & M. Chu n

Contributors: M. Lin* & M. Chu n

author keywords: Entanglement; Separability; Multipartite system; Low-rank approximation; Gradient dynamics; Wirtinger calculus
TL;DR: For the rank-1 approximation, an iterative scheme solving a nonlinear singular value problem is investigated and for the general low-rank approximation with probabilistic combination coefficients, a projected gradient dynamics is proposed. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: April 18, 2022

2022 journal article

Rank-1 Approximation for Entangled Multipartite Real Systems

JOURNAL OF SCIENTIFIC COMPUTING, 91(1).

By: M. Lin* & M. Chu n

Contributors: M. Lin* & M. Chu n

author keywords: Entanglement; Separability; Multipartite system; Low-rank approximation; Nonlinear eigenvalue problem; Nonlinear singular value problem
TL;DR: This paper concerns the approximation over a multipartite system whose subsystems consist of symmetric rank-1 matrices that are entangled via the Kronecker tensor product, except that the discussion in this paper is limited to real-valued matrices. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: March 28, 2022

2021 journal article

NONLINEAR POWER-LIKE AND SVD-LIKE ITERATIVE SCHEMES WITH APPLICATIONS TO ENTANGLED BIPARTITE RANK-1 APPROXIMATION

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 43(5), S448–S474.

By: M. Chu* & M. Lin

Contributors: M. Chu* & M. Lin

author keywords:   entanglement; separability; bipartite system; low-rank approximation; nonlinear eigenvalue problem; nonlinear singular value problem
TL;DR: This work has shown that the distance between a mixed state and the convex set of separable states in a bipartite quantum mechanical system over the complex field is smaller than the total number of states in the system. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID
Added: November 8, 2021

2020 journal article

Nonlinear power-like iteration by polar decomposition and its application to tensor approximation

NUMERISCHE MATHEMATIK, 144(4), 729–749.

By: B. Dong*, N. Jiang* & M. Chu n

Contributors: B. Dong*, N. Jiang* & M. Chu n

TL;DR: This paper proposes a scheme similar to the power method for subspace iterations except that the polar decomposition is used as the normalization process and that the iteration can be applied to both the orbits and the cross-sections. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: April 6, 2020

2019 journal article

Structure-preserving isospectral transformation for total or partial decoupling of self-adjoint quadratic pencils

JOURNAL OF SOUND AND VIBRATION, 449, 157–171.

By: N. Jiang*, M. Chu n & J. Shen*

Contributors: N. Jiang*, M. Chu n & J. Shen*

author keywords: Self-adjoint quadratic pencil; Decoupling; Structure preserving transformation; Lancaster structure; Isospectrality; Gradient flow
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions (OpenAlex)
Sources: Web Of Science, ORCID
Added: April 22, 2019

2018 report

A theoretical consideration of matrix-operative alternating least squares methods for orthogonal CP tensor approximation

[Preprint].

By: M. Chu, Y. Guan, N. Jiang & B. Dong

Source: NC State University Libraries
Added: September 30, 2023

2018 report

Convergence analysis of alternating direction methods: A general framework and its applications to tensor approximations

[Preprint].

By: M. Chu, Y. Guan, B. Dong & N. Jiang

Source: NC State University Libraries
Added: September 30, 2023

2018 journal article

Convergence analysis of an SVD-based algorithm for the best rank-1 tensor approximation

LINEAR ALGEBRA AND ITS APPLICATIONS, 555, 53–69.

By: Y. Guan*, M. Chu n & D. Chu*

Contributors: Y. Guan*, M. Chu n & D. Chu*

author keywords: Best rank-1 tensor approximation; Singular value decomposition
TL;DR: This paper revisits the classical problem of finding the best rank-1 approximation to a generic tensor and proposes a simple tactic to partially close the gap between conventional and SVD algorithms. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: October 19, 2018

2018 report

Decoupling of Lattice Vibration

[Preprint].

By: M. Chu & N. Jiang

Source: NC State University Libraries
Added: September 30, 2023

2018 report

Global rank-1 approximation for order-3 tensors

[Preprint]. https://mtchu.math.ncsu.edu/Research/Papers/Rank1_Order3_Global.pdf

By: M. Chu, N. Jiang & B. Dong

Source: NC State University Libraries
Added: September 30, 2023

2018 journal article

SVD-BASED ALGORITHMS FOR THE BEST RANK-1 APPROXIMATION OF A SYMMETRIC TENSOR

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 39(3), 1095–1115.

By: Y. Guan, M. Chu* & D. Chu

Contributors: Y. Guan, M. Chu* & D. Chu

author keywords: symmetric tensor; best rank-1 approximation; singular value decomposition; convergence analysis
TL;DR: This paper revisits the problem of finding the best rank-1 approximation to a symmetric tensor and makes three contributions. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: January 7, 2019

2017 journal article

Markov chains with memory, tensor formulation, and the dynamics of power iteration

APPLIED MATHEMATICS AND COMPUTATION, 303, 226–239.

By: S. Wu* & M. Chu n

Contributors: S. Wu* & M. Chu n

author keywords: Markov chain with memory; Transition probability tensor; Stationary distribution; Power method; Rate of convergence; Second dominant eigenvalue
TL;DR: Casting the power method as a fixed-point iteration, this paper examines the local behavior of the nonlinear map and identifies the cause of convergence or divergence. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2017 journal article

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

INVERSE PROBLEMS, 33(8).

By: S. Wu* & M. Chu n

Contributors: S. Wu* & M. Chu n

author keywords: inverse eigenvalue problem; majorization relationships; projected gradient; projected Hessian; analytic gradient dynamics
Sources: Web Of Science, ORCID
Added: August 6, 2018

2016 report

A Comment on the best rank-1 approximation of a symmetric tensor

[Preprint].

By: M. Chu

Source: NC State University Libraries
Added: September 30, 2023

2016 report

Numerical Methods for Gradient Dynamics

[Preprint].

By: M. Chu & L. Liao

Source: NC State University Libraries
Added: September 30, 2023

2016 report

On the adjoint of tensors

[Preprint].

By: M. Chu

Source: NC State University Libraries
Added: September 30, 2023

2016 report

On the dynamics of maximin flows

[Preprint].

By: M. Chu

Source: NC State University Libraries
Added: September 30, 2023

2016 journal article

On the first degree Fejer-Riesz factorization and its applications to X plus A*X(-1)A = Q

LINEAR ALGEBRA AND ITS APPLICATIONS, 489, 123–143.

By: M. Chu n

Contributors: M. Chu n

author keywords: Fejer-Riesz factorization; Nonlinear matrix equation; Alternating projection method; Coordinate-free Newton method
Sources: Web Of Science, ORCID
Added: August 6, 2018

2015 journal article

A computational framework of gradient flows for general linear matrix equations

NUMERICAL ALGORITHMS, 68(1), 121–141.

By: L. Wang*, M. Chu n & Y. Bo*

Contributors: L. Wang*, M. Chu n & Y. Bo*

author keywords: Linear matrix equation; Adjoint operator; Least squares; Generalized normal equation; Gradient flow; Low-precision ODE integrator
TL;DR: The flow approach has the advantages of being straightforward for implementation, uniform in theory, versatile in application, working directly with the original sizes without Kronecker vectorization, avoiding inversion or factorization, and being easy for convergence analysis. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2015 journal article

Constructing optimal transition matrix for Markov chain Monte Carlo

LINEAR ALGEBRA AND ITS APPLICATIONS, 487, 184–202.

By: S. Wu* & M. Chu n

Contributors: S. Wu* & M. Chu n

author keywords: MCMC; Asymptotic variance; Stationary distribution; Global optimization; Minimax problem; Inverse eigenvector problem; Stochastic matrix
Sources: Web Of Science, ORCID
Added: August 6, 2018

2015 journal article

ORTHOGONAL LOW RANK TENSOR APPROXIMATION: ALTERNATING LEAST SQUARES METHOD AND ITS GLOBAL CONVERGENCE

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 36(1), 1–19.

By: L. Wang, M. Chu* & B. Yu

Contributors: L. Wang, M. Chu* & B. Yu

author keywords: orthogonal tensor decomposition; low rank approximation; alternating least squares; high-order power method; polar decomposition; global convergence; Zariski topology
TL;DR: The conventional high-order power method is modified to address the desirable orthogonality via the polar decomposition and it is shown that for almost all tensors the orthogonal alternating least squares method converges globally. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2015 journal article

On the finite rank and finite-dimensional representation of bounded semi-infinite Hankel operators

IMA JOURNAL OF NUMERICAL ANALYSIS, 35(3), 1256–1276.

By: M. Chu* & M. Lin*

Contributors: M. Chu* & M. Lin*

author keywords: Hankel operator; semi-infinite matrix; finite rank; Vandermonde factorization; orthogonalization; generating function; LDL* decomposition
Sources: Web Of Science, ORCID
Added: August 6, 2018

2014 journal article

A study of singular spectrum analysis with global optimization techniques

JOURNAL OF GLOBAL OPTIMIZATION, 60(3), 551–574.

By: M. Chu n, M. Lin* & L. Wang*

Contributors: M. Chu n, M. Lin* & L. Wang*

author keywords: Singular spectrum analysis; Time series; Hankel operator; Semi-infinite matrix; Low rank approximation; Vandermonde factorization; Global optimization
TL;DR: The empirical results indicate that the simpler SSA algorithm usually is amazingly sufficient as a handy tool for constructing exploratory model, and the more complicated global methods could be used as an alternative of rigorous affirmative procedure for verifying or assessing the quality of approximation. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2014 journal article

Attaining the Optimal Gaussian Diffusion Acceleration

JOURNAL OF STATISTICAL PHYSICS, 155(3), 571–590.

By: S. Wu*, C. Hwang* & M. Chu n

Contributors: S. Wu*, C. Hwang* & M. Chu n

author keywords: Diffusion acceleration; Convergence to equilibrium; Ornstein-Uhlenbeck process; t-Circulant matrices; Inverse eigenvalue problem; Recursive algorithm; MCMC
TL;DR: Two approaches to obtain the optimal rate of Gaussian diffusion are described: the asymptotical approach works universally for arbitrary Ornstein–Uhlenbeck processes, whereas the direct approach can be implemented as a fast divide-and-conquer algorithm. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2014 journal article

Nonnegative rank factorization-a heuristic approach via rank reduction

NUMERICAL ALGORITHMS, 65(2), 251–274.

By: B. Dong*, M. Lin* & M. Chu n

Contributors: B. Dong*, M. Lin* & M. Chu n

author keywords: Nonnegative matrix; Nonnegative rank; Nonnegative matrix factorization; Nonnegative rank factorization; Wedderburn rank reduction formula; Completely positive matrix; cp-rank
TL;DR: The proposed algorithm might serve as a first-step numerical means for exploring the intriguing problem of nonnegative rank factorization and no convergence can be guaranteed, but repeated restart might help alleviate the difficulty. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2014 journal article

ON THE GLOBAL CONVERGENCE OF THE ALTERNATING LEAST SQUARES METHOD FOR RANK-ONE APPROXIMATION TO GENERIC TENSORS

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 35(3), 1058–1072.

By: L. Wang & M. Chu*

Contributors: L. Wang & M. Chu*

author keywords: tensor decomposition; rank-one tensor approximation; alternating least squares; global convergence; Zariski open set
TL;DR: It is shown that for almost all tensors, the iterates generated by the alternating least squares method for the rank-one approximation converge globally. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2013 journal article

Tensor Spline Approximation in Economic Dynamics with Uncertainties

COMPUTATIONAL ECONOMICS, 42(2), 175–198.

By: M. Chu n, C. Kuo n & M. Lin*

Contributors: M. Chu n, C. Kuo n & M. Lin*

author keywords: Economic dynamics; Dynamic programming; Stochastic uncertainties; Bellman equation; Euler equation; Policy function; Cubic spline; Tensor operation
TL;DR: This note proposes using composite 1-dimensional cubic splines in tensor form to process the Newton iterative scheme on approximating the unknown policy functions, which has the advantages of freedom in the node collocation, simplicity in the derivative calculation, fast convergence, and high precision over the conventional projection methods. (via Semantic Scholar)
UN Sustainable Development Goal Categories
8. Decent Work and Economic Growth (Web of Science; OpenAlex)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2012 journal article

Computing absolute maximum correlation

IMA JOURNAL OF NUMERICAL ANALYSIS, 32(1), 163–184.

By: L. Zhang* & M. Chu*

Contributors: L. Zhang* & M. Chu*

author keywords: multivariate statistics; canonical correlation; multivariate eigenvalue problem; power method; Gauss-Seidal method; global maximizer
TL;DR: Some distinctive traits of theabsolute maximum correlation are characterized and by exploiting these attributes it is possible to propose an effective starting-point strategy that significantly increases the likelihood of attaining the absolute maximum correlation. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2011 journal article

ChemModLab: A web-based cheminformatics modeling laboratory

In Silico Biology, 11(1-2), 61–81.

By: J. Hughes-Oliver n, A. Brooks n, W. Welch*, M. Khaledi n, D. Hawkins*, S. Young*, K. Patil n, G. Howell n, R. Ng*, M. Chu n

Contributors: J. Hughes-Oliver n, A. Brooks n, W. Welch*, M. Khaledi n, D. Hawkins*, S. Young*, K. Patil n, G. Howell n, R. Ng*, M. Chu n

MeSH headings : Data Mining; Informatics / methods; Internet; Models, Molecular; Neural Networks, Computer; Quantitative Structure-Activity Relationship; Software; Support Vector Machine
TL;DR: The capabilities of ChemModLab are illustrated using a variety of biological responses, with different modeling methodologies being applied to each, showing clear differences in quality of the fitted QSAR model, and in computational requirements. (via Semantic Scholar)
Source: ORCID
Added: July 4, 2023

2011 journal article

Dynamical System Characterization of the Central Path and Its Variants-A Revisit

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 10(3), 887–905.

By: M. Chu* & M. Lin

Contributors: M. Chu* & M. Lin

author keywords: linear programming; semidefinite programming; central path; interior point method; projected gradient; dynamical system; affine scaling trajectory
TL;DR: This paper revisits the dynamical system characterization of these flows and addresses the needed details for extension to semidefinite programming by means of a simple notion of operators and a specially defined inner product. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2010 journal article

Inverse mode problems for real and symmetric quadratic models

INVERSE PROBLEMS, 26(6).

By: M. Lin n, B. Dong* & M. Chu n

Contributors: M. Lin n, B. Dong* & M. Chu n

UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID
Added: August 6, 2018

2010 journal article

On the nonnegative rank of Euclidean distance matrices

Linear Algebra and Its Applications, 433(3), 681–689.

By: M. Lin n & M. Chu n

Contributors: M. Lin n & M. Chu n

TL;DR: The Euclidean distance matrix for n distinct points in ℝ r is generically of rank r + 2 and it is shown via a geometric argument that its nonnegative rank for the case r = 1 is generally n. (via Semantic Scholar)
Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2010 report

On the nonnegative rank of Euclidean distance matrices, II

[Preprint].

By: M. Chu

Source: NC State University Libraries
Added: September 30, 2023

2010 journal article

Semi-definite programming techniques for structured quadratic inverse eigenvalue problems

NUMERICAL ALGORITHMS, 53(4), 419–437.

By: M. Lin n, B. Dong* & M. Chu n

Contributors: M. Lin n, B. Dong* & M. Chu n

author keywords: Semi-definite programming; Quadratic pencil; Inverse eigenvalue problem; Structural constraint; Model updating
TL;DR: Of notable interest and significance are the uniformity and the simplicity in the SDP formulation that solves effectively many otherwise very difficult QIEPs. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2009 report

Integer matrix factorization and its applications

[Preprint].

By: M. Chu, M. Lin & B. Dong

Source: NC State University Libraries
Added: September 30, 2023

2009 journal article

Parameter reconstruction of vibration systems from partial eigeninformation

JOURNAL OF SOUND AND VIBRATION, 327(3-5), 391–401.

By: B. Dong*, M. Lin n & M. Chu n

Contributors: B. Dong*, M. Lin n & M. Chu n

TL;DR: A numerical approach is proposed to determine whether the inverse problem is solvable and, if it is so, computes the coefficient matrices while providing an estimate of the residual error. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2009 journal article

QUADRATIC MODEL UPDATING WITH SYMMETRY, POSITIVE DEFINITENESS, AND NO SPILL-OVER

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 31(2), 546–564.

By: D. Chu, M. Chu* & W. Lin

Contributors: D. Chlj, M. Chu* & W. Lin

author keywords: quadratic model; inverse eigenvalue problem; model updating; eigenstructure assignment; spill-over; positive definiteness
TL;DR: Some necessary and sufficient conditions for the solvability conditions are established in this investigation and several theoretical aspects about updating that preserves both no spill-over and positive definiteness of the mass and the stiffness matrices are highlighted. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID
Added: August 6, 2018

2009 journal article

SPECTRAL DECOMPOSITION OF REAL SYMMETRIC QUADRATIC lambda-MATRICES AND ITS APPLICATIONS

MATHEMATICS OF COMPUTATION, 78(265), 293–313.

By: M. Chu n & S. Xu*

Contributors: M. Chu n & X. Shu-Fang

author keywords: Quadratic lambda-matrix; spectral decomposition; real standard pair; inverse eigenvalue problem
TL;DR: The GLR theory is modifies for the special application to real symmetric quadratic matrix polynomials, Q( A) = MX2 + CX + K, M nonsingular, subject to the specific restriction that all matrices in the representation be realvalued. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2008 conference paper

Data mining and applied linear algebra

Proceedings - International Conference on Informatics Education and Research for Knowledge-Circulating Society, ICKS 2008, 20–25.

By: M. Chu n

Contributors: M. Chu n

TL;DR: Examples from factor analysis, cluster analysis, latent semantic indexing and link analysis are used to demonstrate how matrix factorization helps to uncover hidden connection and do things fast. (via Semantic Scholar)
UN Sustainable Development Goal Categories
9. Industry, Innovation and Infrastructure (OpenAlex)
Source: ORCID
Added: July 4, 2023

2008 journal article

Linear algebra algorithms as dynamical systems

Acta Numerica, 17, 1–86.

By: M. Chu n

Contributors: M. Chu n

TL;DR: The notion of dynamical systems as a special realization process for problems arising from the field of linear algebra is exploited to afford unified and fundamental insights into the structure and behaviour of existing discrete methods. (via Semantic Scholar)
Sources: Crossref, ORCID
Added: November 22, 2020

2008 journal article

Low-dimensional polytope approximation and its applications to nonnegative matrix factorization

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 30(3), 1131–1155.

By: M. Chu* & M. Lin

Contributors: M. Chu* & M. Lin

author keywords: nonnegative matrix factorization; polytope approximation; probability simplex; supporting hyperplane; Hahn-Banach theorem
TL;DR: Testing results strongly evidence that this approach obtains a better low rank nonnegative matrix approximation in fewer steps than conventional methods. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2008 journal article

PROJECTED PSEUDOTRANSIENT CONTINUATION

SIAM JOURNAL ON NUMERICAL ANALYSIS, 46(6), 3071–3083.

By: C. Kelley*, L. Liao, L. Qi, M. Chu*, J. Reese* & C. Winton*

Contributors: C. Kelley*, L. Liao, L. Qi, M. Chu*, J. Reese* & C. Winton*

author keywords: pseudotransient continuation; constrained dynamics; gradient flow; bound-constrained optimization; quasi-Newton method
TL;DR: A pseudotransient continuation algorithm for dynamics on subsets of $R^N$. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2008 chapter

Quadratic Inverse Eigenvalue Problem and Its Applications to Model Updating — An Overview

In Mathematics in Industry (pp. 323–340).

By: M. Chu n

TL;DR: This collection of model reduction has been under extensive study and rapid development over the past few years with many physical and engineering applications and the emphasis of the following discussion is on the model updating of quadratic pencils. (via Semantic Scholar)
Sources: Crossref, ORCID
Added: September 22, 2023

2008 chapter

Quadratic inverse eigenvalue problem and its applications to model updating - an overview

In Model Order Reduction: Theory, Research Aspects and Applications.

Contributors: M. Chu

Source: ORCID
Added: August 13, 2023

2008 journal article

Spillover phenomenon in quadratic model updating

AIAA JOURNAL, 46(2), 420–428.

By: M. Chu n, B. Datta*, W. Lin* & S. Xu*

Contributors: M. Chu n, B. Datta*, W. Lin* & S. Xu*

Sources: Web Of Science, ORCID
Added: August 6, 2018

2008 journal article

Total decoupling of general quadratic pencils, Part I: Theory

JOURNAL OF SOUND AND VIBRATION, 309(1-2), 96–111.

By: M. Chu n & N. Del Buono*

Contributors: M. Chu n & N. Del Buono*

UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions (OpenAlex)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2008 journal article

Total decoupling of general quadratic pencils, Part II: Structure preserving isospectral flows

JOURNAL OF SOUND AND VIBRATION, 309(1-2), 112–128.

By: M. Chu n & N. Del Buono*

Contributors: M. Chu n & N. Del Buono*

UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions (OpenAlex)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2007 book

Inverse Eigenvalue Problems: Theory, Algorithms, and Applications

In Inverse Eigenvalue Problems: Theory, Algorithms, and Applications (Vol. 9780198566649, pp. 1–406).

By: M. Chu* & G. Golub

Contributors: M. Chu* & G. Golub

Sources: ORCID, NC State University Libraries
Added: August 6, 2018

2007 journal article

On the estimation of the consumption matrix from inexact data in the leontief model

Journal of Numerical Analysis, Industrial and Applied Mathematics, 2(3-4), 139–156. http://www.scopus.com/inward/record.url?eid=2-s2.0-84947050612&partnerID=MN8TOARS

By: S. Ragni, M. Chu, F. Diele & C. Marangi

Contributors: S. Ragni, M. Chu, F. Diele & C. Marangi

Source: ORCID
Added: July 4, 2023

2007 journal article

Structured quadratic inverse eigenvalue problem, I. Serially linked systems

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 29(6), 2668–2685.

By: M. Chu*, N. Del Buono & B. Yu

Contributors: M. Chu*, N. Del Buono & B. Yu

author keywords: quadratic pencil; inverse eigenvalue problem; linear oscillator; inner-connectivity; nonnegativity; linear system of inequalities
TL;DR: This paper considers one particular structure where the elements of the physical system, if modeled as a mass-spring system, are serially linked and recasts both undamped and damped problems in a framework of inequality systems that can be adapted for numerical computation. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2007 journal article

Updating quadratic models with no spillover effect on unmeasured spectral data

INVERSE PROBLEMS, 23(1), 243–256.

By: M. Chu n, W. Lin* & S. Xu*

Contributors: M. Chu n, W. Lin* & S. Xu*

UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID
Added: August 6, 2018

2006 article

LOW RANK UPDATE OF SINGULAR VALUES

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.6877

By: D. Chu & M. Chu

Source: ORCID
Added: July 4, 2023

2006 journal article

Low rank update of singular values

Mathematics of Computation, 75(255), 1351–1367.

By: D. Chu* & M. Chu n

Contributors: D. Chu* & M. Chu n

author keywords: singular values; low rank update; interlacing properties; pole assignment
TL;DR: This paper deals with the inverse problem of updating a rectangular matrix by additive low rank matrices so as to reposition the associated singular values, analogous to the classical pole assignment problem where eigenvalues of a square matrix are relocated. (via Semantic Scholar)
Sources: Web Of Science, ORCID, Crossref
Added: August 6, 2018

2006 journal article

Reachable matrices by a QR step with shift

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 5(1), 91–107.

By: D. Chu n & M. Chu*

Contributors: D. Chu n & M. Chu*

author keywords: QR algorithm; shift; analytic QR decomposition; reachable matrices; reflexivity; symmetry; transitivity
TL;DR: It is proved that in general the QR algorithm with shift is neither reflexive nor symmetric and the set of all isospectral matrices "reachable" by the dynamics of the algorithm is studied. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2005 article

Nonnegative Matrix Factorization And Applications

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.7507

By: M. Chu & R. Plemmons

Source: ORCID
Added: July 4, 2023

2005 journal article

Nonnegative matrix factorization and applications

IMAGE. https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=73a543613d5eee22fd0172f5c1397ac23d8c09c0

Contributors: M. Chu

Source: ORCID
Added: August 13, 2023

2005 journal article

Nonnegative matrix factorization and applications

IMAGE, 34, 1–5.

By: M. Chu & R. Plemmons

Source: NC State University Libraries
Added: September 30, 2023

2005 journal article

On computing minimal realizable spectral radii of non-negative matrices

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 12(1), 77–86.

By: M. Chu n & S. Xu*

Contributors: M. Chu n & S. Xu*

author keywords: non-negative matrices; Perron-Frobenius theorem; inverse eigenvalue problem; minimal realizable spectral radius; bisection method
TL;DR: This paper proposes a simple bisection procedure to approximate the location of ℛ(ℒ︁) and offers a quick numerical way to check whether a given n‐tuple could be the spectrum of a certain non‐negative matrix. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2005 journal article

On the inverse problem of constructing symmetric pentadiagonal Toeplitz matrices from their three largest eigenvalues

INVERSE PROBLEMS, 21(6), 1879–1894.

By: M. Chu n, F. Diele* & S. Ragni*

Contributors: M. Chu n, F. Diele* & S. Ragni*

Sources: Web Of Science, ORCID
Added: August 6, 2018

2005 journal article

On the low-rank approximation of data on the unit sphere

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 27(1), 46–60.

By: M. Chu*, N. Del Buono, L. Lopez & T. Politi

Contributors: M. Chu*, N. Del Buono, L. Lopez & T. Politi

author keywords: standardized data; linear model; factor analysis; low-rank approximation; latent semantic indexing; projected gradient
TL;DR: An analytic expression of the projected gradient furnishes the first order optimality condition and can be used as a numerical means for solving the problem of best fitting given points on the m-dimensional unit sphere Sm-1 by k-dimensional great circles with k much less than m. (via Semantic Scholar)
Sources: ORCID, Web Of Science
Added: August 6, 2018

2005 report

Optimality, Computation and Interpretation of nonnegative matrix factorizations

[Preprint].

By: M. Chu, F. Diele, R. Plemmons & S. Ragni

Source: NC State University Libraries
Added: September 30, 2023

2004 article

Gradient flow methods for matrix completion with prescribed eigenvalues

Chu, M. T., Diele, F., & Sgura, I. (2004, March 1). LINEAR ALGEBRA AND ITS APPLICATIONS, Vol. 379, pp. 85–112.

By: M. Chu n, F. Diele* & I. Sgura*

Contributors: M. Chu n, F. Diele* & I. Sgura*

author keywords: matrix completion; inverse eigenvalue problem; prescribed entries; isospectral matrices; gradient flow; ODE solvers; restart
Sources: Web Of Science, ORCID
Added: August 6, 2018

2004 report

Group theory, linear transformations, and flows: Dynamical systems on manifolds

[Preprint].

By: M. Chu

Source: NC State University Libraries
Added: September 30, 2023

2004 report

On the least squares Euclidean distance matrix approximation and completion

[Preprint].

By: M. Chu, D. Chu & H. Brown

Source: NC State University Libraries
Added: September 30, 2023

2004 journal article

On the semigroup of standard symplectic matrices and its applications

LINEAR ALGEBRA AND ITS APPLICATIONS, 389(1-3), 215–225.

Contributors: M. Chu n, N. Del Buono*, F. Diele*, T. Politi* & S. Ragni*

author keywords: standard symplectic form; discrete algebraic Riccati equation; structure preserving; power method; block LU decomposition; semigroup
Sources: Web Of Science, ORCID
Added: August 6, 2018

2004 article

SINGULAR VALUE REASSIGNMENT WITH LOW RANK MATRICES

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.71.8290

By: D. Chu & M. Chu

Source: ORCID
Added: July 4, 2023

2004 article

SINGULAR VALUE REASSIGNMENT WITH LOW RANK MATRICES (DRAFT: June 11, 2004)

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.6384

By: D. Chu & M. Chu

Source: ORCID
Added: July 4, 2023

2004 report

The effect of ties on convergence in the k-modes variants for clustering categorical data

[Preprint].

By: M. Chu, N. Orlowski, D. Schlorff, J. Blevins, D. Canas & R. Funderlic

Source: NC State University Libraries
Added: September 30, 2023

2003 journal article

On inverse quadratic eigenvalue problems with partially prescribed eigenstructure

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 25(4), 995–1020.

By: M. Chu*, Y. Kuo & W. Lin

Contributors: M. Chu*, Y. Kuo & W. Lin

author keywords: quadratic eigenvalue problem; inverse eigenvalue problem; partially prescribed spectrum; partial eigenstructure assignment
TL;DR: It is shown via construction that the inverse problem is solvable for any k, given complex conjugately closed pairs of distinct eigenvalues and linearly independent eigenvectors, provided $k \leq n$. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: ORCID, Web Of Science
Added: August 6, 2018

2003 journal article

On robust matrix completion with prescribed eigenvalues

FUTURE GENERATION COMPUTER SYSTEMS, 19(7), 1139–1153.

By: M. Chu n, F. Diele* & I. Sgura*

Contributors: M. Chu n, F. Diele* & I. Sgura*

author keywords: matrix completion; inverse eigenvalue problem; robust solution; isospectral matrices; continuation method; steepest descent gradient flow
TL;DR: This paper investigates some continuation techniques by recasting the completion problem as an optimization of the distance between the isospectral matrices with the prescribed eigenvalues and the affine matriceswith the prescribed entries. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2003 journal article

Real-valued, low rank, circulant approximation

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 24(3), 645–659.

By: M. Chu* & R. Plemmons*

Contributors: M. Chu* & R. Plemmons*

author keywords: real-valued circulant matrix; lower rank; nearest approximation; conjugate-even; fast Fourier transform; truncated singular value decomposition
TL;DR: This paper investigates the case of approximating a given target matrix by a real-valued circulant matrix of a specified, fixed, and low rank by proposing a fast Fourier transform (FFT)-based numerical procedure. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2003 journal article

Structured low rank approximation

LINEAR ALGEBRA AND ITS APPLICATIONS, 366(SPEC. ISS.), 157–172.

By: M. Chu n, R. Funderlic n & R. Plemmons*

Contributors: M. Chu n, R. Funderlic n & R. Plemmons*

author keywords: structured matrix; low rank approximation; optimization techniques; Toeplitz matrix
TL;DR: Two procedures for constructing the nearest structured low rank matrix are proposed and are flexible enough that they can be applied to any lower rank, any linear structure, and any matrix norm in the measurement of nearness. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2002 journal article

Structured inverse eigenvalue problems

Acta Numerica, 11, 1–71.

By: M. Chu n & G. Golub*

Contributors: M. Chu n & G. Golub*

Source: ORCID
Added: July 4, 2023

2002 journal article

The centroid decomposition: Relationships between discrete variational decompositions and SVDs

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 23(4), 1025–1044.

By: M. Chu* & R. Fundelic

Contributors: M. Chu* & R. Funderlic*

author keywords: data matrix; loading matrix; scoring matrix; indexing matrix; factor analysis; centroid method; singular value decomposition; low rank approximation; semidiscrete decomposition; centroid decomposition; low rank decompositions; integer programming
TL;DR: One major purpose of this work is to show fundamental relationships between the singular value, centroid, and semidiscrete decompositions, which unifies an entire class of truncated SVD approximations. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2001 report

On the statistical meaning of truncated singular value decomposition

[Preprint].

By: M. Chu

Source: NC State University Libraries
Added: September 30, 2023

2001 journal article

The orthogonally constrained regression revisited

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS, 10(4), 746–771.

By: M. Chu n & N. Trendafilov n

Contributors: M. Chu n & N. Trendafilov n

author keywords: continuous-time approach; Penrose regression; procrustes rotation; rotation to partially specified target; projected gradient; projected Hessian; optimality conditions
Sources: Web Of Science, ORCID
Added: August 6, 2018

2000 journal article

A fast recursive algorithm for constructing matrices with prescribed eigenvalues and singular values

SIAM JOURNAL ON NUMERICAL ANALYSIS, 37(3), 1004–1020.

By: M. Chu*

Contributors: M. Chu*

author keywords: eigenvalues; singular values; inverse problems; Weyl-Horn theorem; recursive algorithm
TL;DR: A fast recursive algorithm is developed to construct numerically a matrix with prescribed eigenvalues and singular values of an arbitrary matrix based on the Weyl--Horn theorem. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

2000 journal article

A mathematical framework for the linear reconstructor problem in adaptive optics

LINEAR ALGEBRA AND ITS APPLICATIONS, 316(1-3), 113–135.

By: M. Chu n, V. Pauca*, R. Plemmons* & X. Sun*

Contributors: M. Chu n, V. Pauca*, R. Plemmons* & X. Sun*

author keywords: adaptive optics; atmospheric turbulence; deformable mirror; linear reconstruction; minimum variance estimator; adaptive control
UN Sustainable Development Goal Categories
13. Climate Action (Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018

1999 journal article

A Continuous-Time Approach to the Oblique Procrustes Problem

Behaviormetrika, 26(2), 167–181.

By: N. Trendafilov* & M. Chu

Sources: Crossref, ORCID
Added: September 22, 2023

1999 report

On an adaptive control algorithm for the adaptive optics problems

[Preprint].

By: M. Chu

Source: NC State University Libraries
Added: September 30, 2023

1999 journal article

On constructing matrices with prescribed singular values and diagonal elements

LINEAR ALGEBRA AND ITS APPLICATIONS, 288(1-3), 11–22.

By: M. Chu n

Contributors: M. Chu n

UN Sustainable Development Goal Categories
10. Reduced Inequalities (Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018

1998 journal article

A numerical method for the inverse stochastic spectrum problem

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 19(4), 1027–1039.

By: M. Chu* & Q. Guo*

Contributors: M. Chu* & Q. Guo*

author keywords: nonnegative matrix; stochastic matrix; least squares; steepest descent; isospectral flow; structured Markov chain; analytic singular value flow
Sources: Web Of Science, ORCID
Added: August 6, 2018

1998 conference paper

Approximation by structured lower rank matrices

Proceedings of SPIE - The International Society for Optical Engineering, 3461, 268–279.

By: M. Chu n, R. Funderlic n & R. Plemmons*

Contributors: M. Chu n, R. Funderlic n & R. Plemmons*

TL;DR: The techniques developed in this paper can easily be implemented for numerical computation and it is shown that the computations can be approached using efficient optimization packages. (via Semantic Scholar)
Source: ORCID
Added: July 4, 2023

1998 book

Cornelius Lanczos: Collected published papers with commentaries

Raleigh, NC: College of Physical and Mathematical Sciences, North Carolina State University.

By: W. Davis, M. Chu, J. McConnell, P. Dolan, L. Norris, E. Ortiz, R. Plemmon, D. Ridgeway ...

Source: NC State University Libraries
Added: August 6, 2018

1998 review

Inverse eigenvalue problems

[Review of ]. SIAM REVIEW, 40(1), 1–39.

By: M. Chu n

Contributors: M. Chu n

author keywords: eigenvalue problem; inverse problem; parameter estimation; system reconstruction; spectral constraint; structural constraint; iterative methods; direct method; continuous methods; least squares
TL;DR: A collection of inverse eigenvalue problems are identified and classified according to their characteristics, and current developments in both the theoretic and the algorithmic aspects are summarized and reviewed. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

1998 journal article

On a differential equation approach to the weighted or orthogonal Procrustes problem

STATISTICS AND COMPUTING, 8(2), 125–133.

By: M. Chu n & N. Trendafilov*

Contributors: M. Chu n & N. Trendafilov*

author keywords: constrained regression; Procrustes rotation; projected gradient; optimality condition
TL;DR: It is shown that a steepest descent flow on the manifold of orthogonal matrices can naturally be formulated, which has two important implications: that the weighted Orthogonal Procrustes problem can be solved as an initial value problem by any available numerical integrator and that the first order and the second order optimality conditions can also be derived. (via Semantic Scholar)
UN Sustainable Development Goal Categories
4. Quality Education (Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018

1998 journal article

On the least squares approximation of symmetric-definite pencils subject to generalized spectral constraints

SIAM Journal on Matrix Analysis and Applications, 19(1), 1–20.

By: M. Chu* & G. Quanlin

Contributors: M. Chu* & G. Quanlin

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

1998 journal article

On the optimal consistent approximation to pairwise comparison matrices

LINEAR ALGEBRA AND ITS APPLICATIONS, 272(1-3), 155–168.

By: M. Chu n

Contributors: M. Chu n

TL;DR: It is observed that the highly nonlinear manifold of consistent matrices can be changed into a linear subspace by the componentwise logarithmic transformation, which facilitates the otherwise much more complicated optimality condition if working with the variables in the original manifold. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

1998 journal article

Orthomax Rotation Problem. A Differential Equation Approach

Behaviormetrika, 25(1), 13–23.

By: M. Chu n & N. Trendafilov*

Contributors: M. Chu n & N. Trendafilov*

Sources: ORCID, Crossref
Added: July 4, 2023

1998 journal article

Rank modifications of semidefinite matrices associated with a secant update formula

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 20(2), 428–436.

By: M. Chu*, R. Funderlic* & G. Golub

Contributors: M. Chu*, R. Funderlic* & G. Golub

author keywords: rank-one reduction; Wedderburn theorem; BFGS update; DFP update; quasi-Newton methods; rank subtractivity; rank additivity
TL;DR: This paper analyzes rank modification of symmetric positive definite matrices H of the form H + P, where H −M denotes a step of reducing H to a lower-rank, symmetric and positive semidefinite matrix and (H −M) + P denotes astep of restoring H−M to a symmetricpositive definite matrix. (via Semantic Scholar)
Sources: Web Of Science, ORCID
Added: August 6, 2018

1997 journal article

On a variational formulation of the generalized singular value decomposition

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 18(4), 1082–1092.

By: M. Chu*, R. Funderlic* & G. Golub

Contributors: M. Chu*, R. Funderlic* & G. Golub

author keywords: generalized eigenvalue and eigenvector; generalized singular value and singular vector; stationary value and stationary point; deflation; duality
Sources: Web Of Science, ORCID
Added: August 6, 2018

1996 journal article

On the least squares solution of inverse eigenvalue problems

SIAM Journal on Numerical Analysis, 33(6), 2417–2430.

By: X. Chen & M. Chu*

Contributors: X. Chen & M. Chu*

Source: ORCID
Added: July 4, 2023

1995 journal article

A list of matrix flows with applications

Hamiltonian and Gradient Flows, Algorithms and Control, 87–97.

By: M. Chu*

TL;DR: A collection ofrential equations that have been proposed as special continuous realization processes that have potential applications ranging from new development of numerical algorithms to the theoretical solution of open problems are reviewed. (via Semantic Scholar)
Source: Crossref
Added: September 22, 2023

1995 journal article

Constructing a Hermitian Matrix from Its Diagonal Entries and Eigenvalues

SIAM Journal on Matrix Analysis and Applications, 16(1), 207–217.

By: M. Chu*

TL;DR: Two algorithms for determining the matrix numerically are proposed in this paper and, besides its easy implementation, offers a new proof of existence because of its global convergence property. (via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities (Web of Science)
Source: ORCID
Added: August 13, 2023

1995 report

Numerical methods for adaptive-optics systems

[Preprint].

By: M. Chu & R. Plemmons

Source: NC State University Libraries
Added: September 30, 2023

1995 report

On a new geometric meaning of the BFGS update

[Preprint].

By: M. Chu, R. Funderlic & G. Golub

Source: NC State University Libraries
Added: September 30, 2023

1995 report

On the refinement of a Newton method for the inverse Toeplitz eigenvalue Problem

[Preprint].

By: M. Chu

Source: NC State University Libraries
Added: September 30, 2023

1995 journal article

Rank-one reduction formula and its applications to matrix factorizations

SIAM Review, 37(4), 512–530.

By: M. Chu*, R. Funderlic & G. Golub

Contributors: M. Chu*, R. Funderlic & G. Golub

TL;DR: By repeatedly applying the Wedderburn rank-one reduction formula to reduce ranks, a biconjugation process analogous to the Gram–Schmidt process with oblique projections can be developed. (via Semantic Scholar)
Source: ORCID
Added: July 4, 2023

1995 journal article

Scaled Toda-like flows

Linear Algebra and Its Applications, 215(C), 261–273.

By: M. Chu n

Contributors: M. Chu n

UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Source: ORCID
Added: July 4, 2023

1995 journal article

The educational testing problem revisited

IMA Journal of Numerical Analysis, 15(1), 141–160.

By: M. Chu n & J. Wright n

Contributors: M. Chu n & J. Wright n

Source: ORCID
Added: July 4, 2023

1994 chapter

A list of matrix flows with applications

In Hamiltonian and Gradient Flows, Algorithms and Control. https://bookstore.ams.org/fic-3

Contributors: M. Chu

Source: ORCID
Added: August 13, 2023

1994 book

Proceedings of the Cornelius Lanczos International Centenary Conference

Philadelphia, PA: SIAM.

Moody Chu

Ed(s): M. Chu, J. Brown, D. Ellison & R. Plemmons

Source: NC State University Libraries
Added: September 30, 2023

1994 journal article

Symmetric Toeplitz Matrices with Two Prescribed Eigenpairs

SIAM Journal on Matrix Analysis and Applications, 15(2), 623–635.

By: M. Chu* & M. Erbrecht

Source: ORCID
Added: August 13, 2023

1993 journal article

On a Multivariate Eigenvalue Problem, Part I: Algebraic Theory and a Power Method

SIAM Journal on Scientific Computing, 14(5), 1089–1106.

By: M. Chu* & J. Watterson

TL;DR: A convergence property of Horst’s method by forming it as a generalization of the so-called power method is then proved and a closed form on the cardinality of solutions for the multivariate eigenvalue problem is first proved. (via Semantic Scholar)
Source: ORCID
Added: August 13, 2023

1993 report

On the differential equation dX dt = [X; k(X)] where k is a Toeplitz annihilator

[Preprint].

By: M. Chu

Source: NC State University Libraries
Added: October 12, 2023

1993 journal article

The stability group of symmetric Toeplitz matrices

Linear Algebra and Its Applications, 185(C), 119–123.

By: M. Chu n

Contributors: M. Chu n

Source: ORCID
Added: July 4, 2023

1992 journal article

Matrix differential equations: a continuous realization process for linear algebra problems

Nonlinear Analysis, 18(12), 1125–1146.

By: M. Chu n

Contributors: M. Chu n

Source: ORCID
Added: July 4, 2023

1992 journal article

Numerical methods for inverse singular value problems

SIAM Journal on Numerical Analysis, 29(3), 885–903.

By: M. Chu*

Contributors: M. Chu*

Source: ORCID
Added: July 4, 2023

1992 report

On the inverse eigenvalue problem for real circulant matrices

[Preprint].

By: M. Chu

Source: NC State University Libraries
Added: October 12, 2023

1991 journal article

A continuous Jacobi-like approach to the simultaneous reduction of real matrices

Linear Algebra and Its Applications, 147(C), 75–96.

By: M. Chu n

Contributors: M. Chu n

TL;DR: It is shown that the projected gradient of the objective function can be formulated explicitly and gives rise to a system of ordinary differential equations that can be readily solved by numerical software. (via Semantic Scholar)
Source: ORCID
Added: July 4, 2023

1991 journal article

Constructing Symmetric Nonnegative Matrices with Prescribed Eigenvalues by Differential Equations

SIAM Journal on Mathematical Analysis, 22(5), 1372–1387.

By: M. Chu* & K. Driessel

Source: ORCID
Added: August 13, 2023

1991 journal article

Least Squares Approximation by Real Normal Matrices with Specified Spectrum

SIAM Journal on Matrix Analysis and Applications, 12(1), 115–127.

By: M. Chu*

Source: ORCID
Added: August 13, 2023

1990 journal article

Projected gradient method for least squares matrix approximations with spectral constraints

SIAM Journal on Numerical Analysis, 27(4), 1050–1060.

By: M. Chu* & K. Driessel

Contributors: M. Chu* & K. Driessel

Source: ORCID
Added: July 4, 2023

1990 journal article

Solving additive inverse eigenvalue problems for symmetric matrices by the homotopy method

IMA Journal of Numerical Analysis, 10(3), 331–342.

By: M. Chu n

Contributors: M. Chu n

Source: ORCID
Added: July 4, 2023

1990 report

Some numerical experiments with isospectral flows

(Technical Report No. 90-01). Idaho State University.

By: M. Chu & K. Driessel

Source: NC State University Libraries
Added: October 12, 2023

1989 journal article

A numerical method for solving interface problems arising in two-point boundary value problems

Computer Methods in Applied Mechanics and Engineering, 74(1), 99–113.

By: M. Chu* & G. Guiguis

Contributors: M. Chu* & G. Guiguis

TL;DR: A numerical approach iterating on the position of interface points is suggested for solving interface problems arising in two-point boundary value problems, finding that the boundary conditions for each local problem can easily be selected by considering the natural physical requirements. (via Semantic Scholar)
Source: ORCID
Added: July 4, 2023

1989 report

Can real symmetric Toeplitz matrices have arbitrary real spectra?

[Preprint].

By: M. Chu & K. Driessel

Source: NC State University Libraries
Added: October 12, 2023

1988 report

A derivative-free iterative method for locating the hand position of a robot manipulator

(No. MCSP48-0189). Argonne National Laboratory.

By: M. Chu

Source: NC State University Libraries
Added: September 22, 2023

1988 journal article

A note on the homotopy method for linear algebraic eigenvalue problems

Linear Algebra and Its Applications, 105(C), 225–236.

By: M. Chu n

Contributors: M. Chu n

TL;DR: This note offers a simpler proof than Li and Sauer's of the existence of homotopy curves for eigenvalue problems of general matrices for linear algebraic eigen value problems on SIMD machines. (via Semantic Scholar)
Source: ORCID
Added: July 4, 2023

1988 journal article

Homotopy Method for General $\lambda $-Matrix Problems

SIAM Journal on Matrix Analysis and Applications, 9(4), 528–536.

By: M. Chu*, T. Li & T. Sauer

TL;DR: The homotopy method might be used to find all isolated eigenpairs for large-scale $\lambda $-matrix problems on single-instruction multiple data (SIMD) machines. (via Semantic Scholar)
Source: ORCID
Added: August 13, 2023

1988 journal article

Isospectral Flows and Abstract Matrix Factorizations

SIAM Journal on Numerical Analysis, 25(6), 1383–1391.

By: M. Chu* & L. Norris

TL;DR: The proposed theory unifies as special cases the well-known matrix decomposition techniques used in numerical linear algebra and is likely to offer a broader approach to the general matrix factorization problem. (via Semantic Scholar)
UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Source: ORCID
Added: August 13, 2023

1988 journal article

On the continuous realization of iterative processes

SIAM Review, 30(3), 375–387.

By: M. Chu*

Contributors: M. Chu*

TL;DR: This paper summarizes some of the recent developments in the continuous realization of several popular basic iterative methods. (via Semantic Scholar)
UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Source: ORCID
Added: July 4, 2023

1987 report

On a differential equation approach to the additive inverse eigenvalue problems

[Preprint].

By: M. Chu

Source: NC State University Libraries
Added: October 12, 2023

1987 journal article

Parallel Solution of ODE’<scp>s</scp> by Multiblock Methods

SIAM Journal on Scientific and Statistical Computing, 8(3), 342–353.

By: M. Chu* & H. Hamilton

TL;DR: The notion of linear multi-step methods for solving ordinary differential equations is generalized to a class of multi-block methods where step values are all obtained together in a single block advance by allocating the parallel tasks on separate processors. (via Semantic Scholar)
Source: ORCID
Added: August 13, 2023

1987 report

Some remarks on the zero-stability of multiblock methods

[Preprint].

By: M. Chu & H. Hamilton

Source: NC State University Libraries
Added: October 12, 2023

1986 journal article

A continuous approximation to the generalized Schur decomposition

Linear Algebra and Its Applications, 78(C), 119–132.

By: M. Chu n

Contributors: M. Chu n

UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Source: ORCID
Added: July 4, 2023

1986 journal article

A differential equation approach to the singular value decomposition of bidiagonal matrices

Linear Algebra and Its Applications, 80(C), 71–79.

By: M. Chu n

Contributors: M. Chu n

UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Source: ORCID
Added: July 4, 2023

1986 report

Continuous power method

[Preprint].

By: M. Chu

Source: NC State University Libraries
Added: October 12, 2023

1986 journal article

Curves on $S^{n - 1} $ That Lead to Eigenvalues or Their Means of a Matrix

SIAM Journal on Algebraic Discrete Methods, 7(3), 425–432.

By: M. Chu*

UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Source: ORCID
Added: August 13, 2023

1985 journal article

Asymptotic analysis of Toda lattice on diagonalizable matrices

Nonlinear Analysis, 9(2), 193–201.

By: M. Chu*

Contributors: M. Chu*

UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Source: ORCID
Added: July 4, 2023

1985 journal article

Symbolic calculation of the trace of the power of a tridiagonal matrix

Computing, 35(3-4), 257–268.

By: M. Chu n

Contributors: M. Chu n

TL;DR: An algorithm symbolically calculating the trace of the power of a tridiagonal matrix is proposed, based on techniques developed from structure analysis and combinatorics. (via Semantic Scholar)
Source: ORCID
Added: July 4, 2023

1984 journal article

A simple application of the homotopy method to symmetric eigenvalue problems

Linear Algebra and Its Applications, 59(C), 85–90.

By: M. Chu n

Contributors: M. Chu n

TL;DR: It is shown that there are exactly n distinct smooth curves connecting trivial solutions to desired eigenpairs and these curves are solutions of a certain ordinary differential equation with different initial values. (via Semantic Scholar)
Source: ORCID
Added: July 4, 2023

1984 journal article

On the Global Convergence of the Toda Lattice for Real Normal Matrices and Its Applications to the Eigenvalue Problem

SIAM Journal on Mathematical Analysis, 15(1), 98–104.

By: M. Chu*

Contributors: M. Chu*

UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Sources: ORCID, Crossref
Added: August 13, 2023

1984 journal article

The Generalized Toda Flow, the QR Algorithm and the Center Manifold Theory

SIAM Journal on Algebraic Discrete Methods, 5(2), 187–201.

By: M. Chu*

UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Source: ORCID
Added: August 13, 2023

1983 journal article

An automatic multistep method for solving stiff initial value problems

Journal of Computational and Applied Mathematics, 9(3), 229–238.

By: M. Chu n

Contributors: M. Chu n

TL;DR: A multistep method with matricial coefficients that can be used to solve stiff initial value problems of the form y? (via Semantic Scholar)
Source: ORCID
Added: July 4, 2023

1983 journal article

On a numerical treatment for the curve-tracing of the homotopy method

Numerische Mathematik, 42(3), 323–329.

By: M. Chu n

Contributors: M. Chu n

Source: ORCID
Added: July 4, 2023

article

Data Mining and Applied Linear Algebra

Chu, M. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.6302

By: M. Chu

Source: ORCID
Added: July 4, 2023

article

Low Rank Circulant Approximation

Plemmonsy, M. C. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.6788

By: M. Plemmonsy

Source: ORCID
Added: July 4, 2023

article

REAL SYMMETRIC QUADRATIC MODEL UPDATING THAT PRESERVES POSITIVE DEFINITENESS AND NO SPILL-OVER

Chu, D., Chu, M., & Lin, W.-wei. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.5746

By: D. Chu, M. Chu & W. Lin

Source: ORCID
Added: July 4, 2023

article

Rank Modifications Of Semi-Definite Matrices With Applications To Secant Updates

Chu, M., Funderlic, R. E., Gene, & Golub, H. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.6137

By: M. Chu, R. Funderlic, Gene & H. Golub

Source: ORCID
Added: July 4, 2023

Funding History

Funding history based on the linked ORCID record. Updated: March 1st, 2024 16:13

grant September 1, 2023 - August 31, 2026
Preparing Hamiltonians for Quantum Simulation: A Computational Framework for Cartan Decomposition via Lax Dynamics
Directorate for Mathematical & Physical Sciences
grant July 1, 2019 - June 30, 2022
From Quantum Entanglement to Tensor Decomposition by Global Optimization
Directorate for Mathematical & Physical Sciences
grant September 15, 2013 - August 31, 2017
Numerical Algorithms as Dynamcal Systems - Structure Preservation, Convergence Theory, and Rediscretization
Directorate for Mathematical & Physical Sciences
grant September 1, 2010 - August 31, 2014
Automated Structure Generation, Error Correction, and Semi-Definite Programming Techniques for Structured Quadratic Inverse Eigenvale Problems: Theory, Algorithms and Applications
Directorate for Mathematical & Physical Sciences
grant October 1, 2007 - September 30, 2011
MSPA-MCS: Collaborative Research: Fast Nonnegative Matrix Factorizations: Theory, Algorithms, and Applications
Directorate for Computer & Information Science & Engineering
grant August 1, 2005 - July 31, 2010
Collaborative Proposal: Quadratic Inverse Eigenvalue Problems for Model Updating in Science and Engineering: Theory and Computation
Directorate for Mathematical & Physical Sciences
grant July 1, 2002 - June 30, 2007
The Centroid Decomposition and Other Approximations to the SVD
Directorate for Computer & Information Science & Engineering
grant August 1, 2000 - July 31, 2004
Algorithms for the Inverse Problem of Matrix Construction
Directorate for Mathematical & Physical Sciences
grant July 1, 1998 - May 31, 2002
Adaptive Control Algorithms for Adaptive Optics Applications
Directorate for Mathematical & Physical Sciences
grant May 15, 1995 - April 30, 1999
Mathematical Sciences: Inverse Eigenvalue Problems
Directorate for Mathematical & Physical Sciences
grant June 1, 1993 - November 30, 1994
Mathematical Sciences: Lanczos International Centenary Conference
Directorate for Mathematical & Physical Sciences
grant July 1, 1992 - June 30, 1996
Mathematical Sciences: Matrix Differential Equations and Their Applications
Directorate for Mathematical & Physical Sciences
grant July 1, 1990 - December 31, 1992
Mathematical Sciences: Matrix Differential Equations and Their Applications
Directorate for Mathematical & Physical Sciences
grant July 1, 1986 - June 30, 1988
Mathematical Sciences: Parallel Multi-Block Methods for Ordinary Differential Equations
Directorate for Mathematical & Physical Sciences

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