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.
author keywords: Borsuk-Ulam theorem; Hypercubes; Generic coordinates; Homeomorphism; Spherical mean
Sources: Web Of Science, NC State University Libraries
Added: January 29, 2024
2023 journal article
An Innate Moving Frame on Parametric Surfaces: The Dynamics of Principal Singular Curves
Mathematics, 11(15), 3306.
author keywords: moving frame; nonlinear variation; gradient adaption; singular curves; critical curves; base pairings; parametric surfaces; geometric genome
www.mdpi.com (publisher PDF)
Sources: ORCID, Web Of Science, NC State University Libraries, 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.
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, NC State University Libraries, 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.
Contributors: n & M. Lin *
author keywords: Quantum states; Entanglement; Separability; Bipartite system; Low-rank approximation; Gradient dynamics; Wirtinger calculus
UN Sustainable Development Goal Categories
9. Industry, Innovation and Infrastructure
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: March 7, 2022
2022 journal article
Low-rank approximation to entangled multipartite quantum systems
QUANTUM INFORMATION PROCESSING, 21(4).
Contributors: M. Lin * & 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, NC State University Libraries
Added: April 18, 2022
2022 journal article
Rank-1 Approximation for Entangled Multipartite Real Systems
JOURNAL OF SCIENTIFIC COMPUTING, 91(1).
Contributors: M. Lin * & 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, NC State University Libraries
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.
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
9. Industry, Innovation and Infrastructure
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
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.
Contributors: B. Dong *, N. Jiang * & 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, NC State University Libraries
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.
Contributors: N. Jiang *, n & J. Shen *
author keywords: Self-adjoint quadratic pencil; Decoupling; Structure preserving transformation; Lancaster structure; Isospectrality; Gradient flow
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
16. Peace, Justice and Strong Institutions
(OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: April 22, 2019
2018 report
A theoretical consideration of matrix-operative alternating least squares methods for orthogonal CP tensor approximation
[Preprint].
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].
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.
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, NC State University Libraries
Added: October 19, 2018
2018 report
Decoupling of Lattice Vibration
[Preprint].
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
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.
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, NC State University Libraries
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.
Contributors: S. Wu * & 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, NC State University Libraries
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).
Contributors: S. Wu * & n
author keywords: inverse eigenvalue problem; majorization relationships; projected gradient; projected Hessian; analytic gradient dynamics
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2016 report
A Comment on the best rank-1 approximation of a symmetric tensor
[Preprint].
Source: NC State University Libraries
Added: September 30, 2023
2016 report
Numerical Methods for Gradient Dynamics
[Preprint].
Source: NC State University Libraries
Added: September 30, 2023
2016 report
On the adjoint of tensors
[Preprint].
Source: NC State University Libraries
Added: September 30, 2023
2016 report
On the dynamics of maximin flows
[Preprint].
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.
author keywords: Fejer-Riesz factorization; Nonlinear matrix equation; Alternating projection method; Coordinate-free Newton method
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2015 journal article
A computational framework of gradient flows for general linear matrix equations
NUMERICAL ALGORITHMS, 68(1), 121–141.
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, NC State University Libraries
Added: August 6, 2018
2015 journal article
Constructing optimal transition matrix for Markov chain Monte Carlo
LINEAR ALGEBRA AND ITS APPLICATIONS, 487, 184–202.
Contributors: S. Wu * & n
author keywords: MCMC; Asymptotic variance; Stationary distribution; Global optimization; Minimax problem; Inverse eigenvector problem; Stochastic matrix
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
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.
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, NC State University Libraries
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.
Contributors: * & M. Lin *
author keywords: Hankel operator; semi-infinite matrix; finite rank; Vandermonde factorization; orthogonalization; generating function; LDL* decomposition
Sources: Web Of Science, ORCID, NC State University Libraries
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.
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, NC State University Libraries
Added: August 6, 2018
2014 journal article
Attaining the Optimal Gaussian Diffusion Acceleration
JOURNAL OF STATISTICAL PHYSICS, 155(3), 571–590.
Contributors: S. Wu *, C. Hwang* & 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, NC State University Libraries
Added: August 6, 2018
2014 journal article
Nonnegative rank factorization-a heuristic approach via rank reduction
NUMERICAL ALGORITHMS, 65(2), 251–274.
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, NC State University Libraries
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.
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, NC State University Libraries
Added: August 6, 2018
2013 journal article
Tensor Spline Approximation in Economic Dynamics with Uncertainties
COMPUTATIONAL ECONOMICS, 42(2), 175–198.
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, NC State University Libraries
Added: August 6, 2018
2012 journal article
Computing absolute maximum correlation
IMA JOURNAL OF NUMERICAL ANALYSIS, 32(1), 163–184.
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, NC State University Libraries
Added: August 6, 2018
2011 journal article
ChemModLab: A web-based cheminformatics modeling laboratory
In Silico Biology, 11(1-2), 61–81.
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*, 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.
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, NC State University Libraries
Added: August 6, 2018
2010 journal article
Inverse mode problems for real and symmetric quadratic models
INVERSE PROBLEMS, 26(6).
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2010 journal article
On the nonnegative rank of Euclidean distance matrices
Linear Algebra and Its Applications, 433(3), 681–689.
Contributors: M. Lin n & 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, NC State University Libraries
Added: August 6, 2018
2010 report
On the nonnegative rank of Euclidean distance matrices, II
[Preprint].
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.
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)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2009 report
Integer matrix factorization and its applications
[Preprint].
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.
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)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
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.
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
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
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.
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)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
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.
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
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, NC State University Libraries
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.
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, NC State University Libraries, ORCID
Added: August 6, 2018
2008 journal article
PROJECTED PSEUDOTRANSIENT CONTINUATION
SIAM JOURNAL ON NUMERICAL ANALYSIS, 46(6), 3071–3083.
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, NC State University Libraries
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).
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, NC State University Libraries
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.
Source: ORCID
Added: August 13, 2023
2008 journal article
Spillover phenomenon in quadratic model updating
AIAA JOURNAL, 46(2), 420–428.
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
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.
Contributors: n & N. Del Buono *
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
16. Peace, Justice and Strong Institutions
(OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
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.
Contributors: n & N. Del Buono *
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
16. Peace, Justice and Strong Institutions
(OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
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).
Sources: ORCID, NC State University Libraries, 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
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.
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)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2007 journal article
Updating quadratic models with no spillover effect on unmeasured spectral data
INVERSE PROBLEMS, 23(1), 243–256.
Contributors: n , W. Lin * & S. Xu*
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
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
Source: ORCID
Added: July 4, 2023
2006 journal article
Low rank update of singular values
Mathematics of Computation, 75(255), 1351–1367.
Contributors: D. 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, NC State University Libraries, 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.
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, NC State University Libraries
Added: August 6, 2018
2005 article
Nonnegative Matrix Factorization And Applications
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.7507
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
Source: ORCID
Added: August 13, 2023
2005 journal article
Nonnegative matrix factorization and applications
IMAGE, 34, 1–5.
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.
Contributors: 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, NC State University Libraries
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.
Contributors: n , F. Diele * & S. Ragni *
Sources: Web Of Science, ORCID, NC State University Libraries
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.
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, NC State University Libraries
Added: August 6, 2018
2005 report
Optimality, Computation and Interpretation of nonnegative matrix factorizations
[Preprint].
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.
Contributors: 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, NC State University Libraries
Added: August 6, 2018
2004 report
Group theory, linear transformations, and flows: Dynamical systems on manifolds
[Preprint].
Source: NC State University Libraries
Added: September 30, 2023
2004 report
On the least squares Euclidean distance matrix approximation and completion
[Preprint].
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: , 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, NC State University Libraries
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
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
Source: ORCID
Added: July 4, 2023
2004 report
The effect of ties on convergence in the k-modes variants for clustering categorical data
[Preprint].
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.
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
11. Sustainable Cities and Communities
(Web of Science)
Sources: ORCID, Web Of Science, NC State University Libraries
Added: August 6, 2018
2003 journal article
On robust matrix completion with prescribed eigenvalues
FUTURE GENERATION COMPUTER SYSTEMS, 19(7), 1139–1153.
Contributors: 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, NC State University Libraries
Added: August 6, 2018
2003 journal article
Real-valued, low rank, circulant approximation
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 24(3), 645–659.
Contributors: * & 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, NC State University Libraries
Added: August 6, 2018
2003 journal article
Structured low rank approximation
LINEAR ALGEBRA AND ITS APPLICATIONS, 366(SPEC. ISS.), 157–172.
Contributors: 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, NC State University Libraries
Added: August 6, 2018
2002 journal article
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.
Contributors: * & 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, NC State University Libraries
Added: August 6, 2018
2001 report
On the statistical meaning of truncated singular value decomposition
[Preprint].
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.
author keywords: continuous-time approach; Penrose regression; procrustes rotation; rotation to partially specified target; projected gradient; projected Hessian; optimality conditions
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
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.
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)
UN Sustainable Development Goal Categories
10. Reduced Inequalities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
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.
Contributors: 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, NC State University Libraries
Added: August 6, 2018
1999 journal article
A Continuous-Time Approach to the Oblique Procrustes Problem
Behaviormetrika, 26(2), 167–181.
Sources: Crossref, NC State University Libraries
Added: September 22, 2023
1999 report
On an adaptive control algorithm for the adaptive optics problems
[Preprint].
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.
UN Sustainable Development Goal Categories
10. Reduced Inequalities
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
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.
Contributors: * & 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, NC State University Libraries
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.
Contributors: 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.
Source: NC State University Libraries
Added: August 6, 2018
1998 review
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, NC State University Libraries
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.
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, NC State University Libraries
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.
Sources: NC State University Libraries, ORCID, NC State University Libraries
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.
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, NC State University Libraries
Added: August 6, 2018
1998 journal article
Orthomax Rotation Problem. A Differential Equation Approach
Behaviormetrika, 25(1), 13–23.
Sources: ORCID, Crossref, NC State University Libraries
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.
Contributors: * , 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, NC State University Libraries
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.
Contributors: * , 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, NC State University Libraries
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.
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.
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.
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].
Source: NC State University Libraries
Added: September 30, 2023
1995 report
On a new geometric meaning of the BFGS update
[Preprint].
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].
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.
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
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.
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
Source: ORCID
Added: August 13, 2023
1994 book
Proceedings of the Cornelius Lanczos International Centenary Conference
Philadelphia, PA: SIAM.
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.
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.
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].
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.
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.
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.
Source: ORCID
Added: July 4, 2023
1992 report
On the inverse eigenvalue problem for real circulant matrices
[Preprint].
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.
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.
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.
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.
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.
Source: ORCID
Added: July 4, 2023
1990 report
Some numerical experiments with isospectral flows
(Technical Report No. 90-01). Idaho State University.
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.
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].
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.
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.
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.
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.
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
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].
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.
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].
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.
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.
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
Source: ORCID
Added: July 4, 2023
1986 report
Continuous power method
[Preprint].
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.
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.
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.
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.
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.
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.
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.
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.
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
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
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
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
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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