Moody Ten-Chao Chu

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

Mathematics, 11(15), 3306.

Lax dynamics for Cartan decomposition with applications to Hamiltonian simulation

IMA Journal of Numerical Analysis, 4, drad018.

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

COMPUTER PHYSICS COMMUNICATIONS, 271.

Low-rank approximation to entangled multipartite quantum systems

QUANTUM INFORMATION PROCESSING, 21(4).

Rank-1 Approximation for Entangled Multipartite Real Systems

JOURNAL OF SCIENTIFIC COMPUTING, 91(1).

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.

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

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

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

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

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

[Preprint].

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

[Preprint].

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

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

Decoupling of Lattice Vibration

[Preprint].

Global rank-1 approximation for order-3 tensors

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

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

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

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

APPLIED MATHEMATICS AND COMPUTATION, 303, 226–239.

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

INVERSE PROBLEMS, 33(8).

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

[Preprint].

Numerical Methods for Gradient Dynamics

[Preprint].

On the adjoint of tensors

[Preprint].

On the dynamics of maximin flows

[Preprint].

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.

A computational framework of gradient flows for general linear matrix equations

NUMERICAL ALGORITHMS, 68(1), 121–141.

Constructing optimal transition matrix for Markov chain Monte Carlo

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

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

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

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

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

A study of singular spectrum analysis with global optimization techniques

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

Attaining the Optimal Gaussian Diffusion Acceleration

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

Nonnegative rank factorization-a heuristic approach via rank reduction

NUMERICAL ALGORITHMS, 65(2), 251–274.

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.

Tensor Spline Approximation in Economic Dynamics with Uncertainties

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

Computing absolute maximum correlation

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

ChemModLab: A web-based cheminformatics modeling laboratory

In Silico Biology, 11(1-2), 61–81.

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

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

Inverse mode problems for real and symmetric quadratic models

INVERSE PROBLEMS, 26(6).

On the nonnegative rank of Euclidean distance matrices

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

On the nonnegative rank of Euclidean distance matrices, II

[Preprint].

Semi-definite programming techniques for structured quadratic inverse eigenvalue problems

NUMERICAL ALGORITHMS, 53(4), 419–437.

Integer matrix factorization and its applications

[Preprint].

Parameter reconstruction of vibration systems from partial eigeninformation

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

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

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

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

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

Data mining and applied linear algebra

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

Linear algebra algorithms as dynamical systems

Acta Numerica, 17, 1–86.

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

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

PROJECTED PSEUDOTRANSIENT CONTINUATION

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

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

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

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

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

Spillover phenomenon in quadratic model updating

AIAA JOURNAL, 46(2), 420–428.

Total decoupling of general quadratic pencils, Part I: Theory

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

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

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

Inverse Eigenvalue Problems: Theory, Algorithms, and Applications

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

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

Structured quadratic inverse eigenvalue problem, I. Serially linked systems

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

Updating quadratic models with no spillover effect on unmeasured spectral data

INVERSE PROBLEMS, 23(1), 243–256.

LOW RANK UPDATE OF SINGULAR VALUES

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

Low rank update of singular values

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

Reachable matrices by a QR step with shift

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

Nonnegative Matrix Factorization And Applications

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

Nonnegative matrix factorization and applications

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

Nonnegative matrix factorization and applications

IMAGE, 34, 1–5.

On computing minimal realizable spectral radii of non-negative matrices

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

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

INVERSE PROBLEMS, 21(6), 1879–1894.

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

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

Optimality, Computation and Interpretation of nonnegative matrix factorizations

[Preprint].

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.

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

[Preprint].

On the least squares Euclidean distance matrix approximation and completion

[Preprint].

On the semigroup of standard symplectic matrices and its applications

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

SINGULAR VALUE REASSIGNMENT WITH LOW RANK MATRICES

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

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

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

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

[Preprint].

On inverse quadratic eigenvalue problems with partially prescribed eigenstructure

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

On robust matrix completion with prescribed eigenvalues

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

Real-valued, low rank, circulant approximation

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

Structured low rank approximation

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

Structured inverse eigenvalue problems

Acta Numerica, 11, 1–71.

The centroid decomposition: Relationships between discrete variational decompositions and SVDs

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

On the statistical meaning of truncated singular value decomposition

[Preprint].

The orthogonally constrained regression revisited

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

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

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

A mathematical framework for the linear reconstructor problem in adaptive optics

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

A Continuous-Time Approach to the Oblique Procrustes Problem

Behaviormetrika, 26(2), 167–181.

On an adaptive control algorithm for the adaptive optics problems

[Preprint].

On constructing matrices with prescribed singular values and diagonal elements

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

A numerical method for the inverse stochastic spectrum problem

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

Approximation by structured lower rank matrices

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

Cornelius Lanczos: Collected published papers with commentaries

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

Inverse eigenvalue problems

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

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

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

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.

On the optimal consistent approximation to pairwise comparison matrices

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

Orthomax Rotation Problem. A Differential Equation Approach

Behaviormetrika, 25(1), 13–23.

Rank modifications of semidefinite matrices associated with a secant update formula

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

On a variational formulation of the generalized singular value decomposition

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

On the least squares solution of inverse eigenvalue problems

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

A list of matrix flows with applications

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

Constructing a Hermitian Matrix from Its Diagonal Entries and Eigenvalues

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

Numerical methods for adaptive-optics systems

[Preprint].

On a new geometric meaning of the BFGS update

[Preprint].

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

[Preprint].

Rank-one reduction formula and its applications to matrix factorizations

SIAM Review, 37(4), 512–530.

Scaled Toda-like flows

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

The educational testing problem revisited

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

A list of matrix flows with applications

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

Proceedings of the Cornelius Lanczos International Centenary Conference

Philadelphia, PA: SIAM.

Symmetric Toeplitz Matrices with Two Prescribed Eigenpairs

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

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

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

The stability group of symmetric Toeplitz matrices

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

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

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

Numerical methods for inverse singular value problems

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

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

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

Constructing Symmetric Nonnegative Matrices with Prescribed Eigenvalues by Differential Equations

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

Least Squares Approximation by Real Normal Matrices with Specified Spectrum

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

Projected gradient method for least squares matrix approximations with spectral constraints

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

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

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

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.

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

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

A note on the homotopy method for linear algebraic eigenvalue problems

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

Homotopy Method for General $\lambda $-Matrix Problems

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

Isospectral Flows and Abstract Matrix Factorizations

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

On the continuous realization of iterative processes

SIAM Review, 30(3), 375–387.

Parallel Solution of ODE’s by Multiblock Methods

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

A continuous approximation to the generalized Schur decomposition

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

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

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

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.

Asymptotic analysis of Toda lattice on diagonalizable matrices

Nonlinear Analysis, 9(2), 193–201.

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

Computing, 35(3-4), 257–268.

A simple application of the homotopy method to symmetric eigenvalue problems

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

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.

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

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

An automatic multistep method for solving stiff initial value problems

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

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

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

Data Mining and Applied Linear Algebra

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

Low Rank Circulant Approximation

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

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

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