Moody Ten-Chao Chu

Generalized Gentlest Ascent Dynamics Methods for High-Index Saddle Points

Chu, M. T., & Lin, M. M. (2025, November 19). SIAM Journal on Numerical Analysis.

On the Refinement of Cartan Decomposition: An Implicit Commutative Substructure in $$\mathfrak {su}(2^{n})$$

Chu, M. (2025, July 19). Results in Mathematics, Vol. 80.

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.

Preparing Hamiltonians for quantum simulation: A computational framework for Cartan decomposition via Lax dynamics

Chu, M. (2024, December 11). Mathematics of Computation, Vol. 2.

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.

Low-rank approximation to entangled multipartite quantum systems

Lin, M. M., & Chu, M. T. (2022, March 30). Quantum Information Processing, Vol. 21.

Rank-1 Approximation for Entangled Multipartite Real Systems

Lin, M. M., & Chu, M. T. (2022, March 7). Journal of Scientific Computing, Vol. 91.

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

Chu, M. T., & Lin, M. M. (2021, October 13). Computer Physics Communications, Vol. 271.

Nonlinear Power-Like and SVD-Like Iterative Schemes with Applications to Entangled Bipartite Rank-1 Approximation

Chu, M. T., & Lin, M. M. (2021, January 1). SIAM Journal on Scientific Computing, Vol. 43, pp. S448–S474.

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

Dong, B., Jiang, N., & Chu, M. T. (2020, February 8). Numerische Mathematik, Vol. 144, pp. 729–749.

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

Jiang, N., Chu, M. T., & Shen, J. (2019, February 16). Journal of Sound and Vibration, Vol. 449, pp. 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

Guan, Y., Chu, M. T., & Chu, D. (2018, June 6). Linear Algebra and Its Applications, Vol. 555, pp. 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

Guan, Y., Chu, M. T., & Chu, D. (2018, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 39, pp. 1095–1115.

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

Wu, S.-J., & Chu, M. T. (2017, February 2). Applied Mathematics and Computation, Vol. 303, pp. 226–239.

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

Wu, S.-J., & Chu, M. T. (2017, June 2). Inverse Problems, Vol. 33.

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].

Constructing optimal transition matrix for Markov chain Monte Carlo

Wu, S.-J., & Chu, M. T. (2015, September 21). Linear Algebra and Its Applications, Vol. 487, pp. 184–202.

On the first degree Fejér–Riesz factorization and its applications to X+A⁎X−1A=Q

Chu, M. T. (2015, November 17). Linear Algebra and Its Applications, Vol. 489, pp. 123–143.

Orthogonal Low Rank Tensor Approximation: Alternating Least Squares Method and Its Global Convergence

Wang, L., Chu, M. T., & Yu, B. (2015, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 36, pp. 1–19.

A computational framework of gradient flows for general linear matrix equations

Wang, L., Chu, M. T., & Bo, Y. (2014, July 9). Numerical Algorithms, Vol. 68, pp. 121–141.

Attaining the Optimal Gaussian Diffusion Acceleration

Wu, S.-J., Hwang, C.-R., & Chu, M. T. (2014, March 17). Journal of Statistical Physics, Vol. 155, pp. 571–590.

On the Global Convergence of the Alternating Least Squares Method for Rank-One Approximation to Generic Tensors

Wang, L., & Chu, M. T. (2014, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 35, pp. 1058–1072.

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

Chu, M. T., & Lin, M. M. (2014, July 1). IMA Journal of Numerical Analysis, Vol. 35, pp. 1256–1276.

A study of singular spectrum analysis with global optimization techniques

Chu, M. T., Lin, M. M., & Wang, L. (2013, October 12). Journal of Global Optimization, Vol. 60, pp. 551–574.

Nonnegative rank factorization—a heuristic approach via rank reduction

Dong, B., Lin, M. M., & Chu, M. T. (2013, March 26). Numerical Algorithms, Vol. 65, pp. 251–274.

ChemModLab: A Web-Based Cheminformatics Modeling Laboratory

Hughes-Oliver, J. M., Brooks, A. D., Welch, W. J., Khaledi, M. G., Hawkins, D., Young, S. S., … Chu, M. T. (2012, January 1). In Silico Biology, Vol. 11, pp. 61–81.

Tensor Spline Approximation in Economic Dynamics with Uncertainties

Chu, M. T., Kuo, C.-H., & Lin, M. M. (2012, June 17). Computational Economics, Vol. 42, pp. 175–198.

Computing absolute maximum correlation

Zhang, L.-H., & Chu, M. T. (2011, May 27). IMA Journal of Numerical Analysis, Vol. 32, pp. 163–184.

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

Chu, M. T., & Lin, M. M. (2011, January 1). SIAM Journal on Applied Dynamical Systems, Vol. 10, pp. 887–905.

Inverse mode problems for real and symmetric quadratic models

Lin, M. M., Dong, B., & Chu, M. T. (2010, May 14). Inverse Problems, Vol. 26.

On the nonnegative rank of Euclidean distance matrices

Lin, M. M., & Chu, M. T. (2010, April 26). Linear Algebra and Its Applications, Vol. 433, pp. 681–689.

On the nonnegative rank of Euclidean distance matrices, II

[Preprint].

Integer matrix factorization and its applications

[Preprint].

Parameter reconstruction of vibration systems from partial eigeninformation

Dong, B., Lin, M. M., & Chu, M. T. (2009, August 4). Journal of Sound and Vibration, Vol. 327, pp. 391–401.

Quadratic Model Updating with Symmetry, Positive Definiteness, and No Spill-Over

Chu, D., Chu, M., & Lin, W.-W. (2009, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 31, pp. 546–564.

Semi-definite programming techniques for structured quadratic inverse eigenvalue problems

Lin, M. M., Dong, B., & Chu, M. T. (2009, July 15). Numerical Algorithms, Vol. 53, pp. 419–437.

Data Mining and Applied Linear Algebra

Chu, M. (2008, January 1). Proceedings - International Conference on Informatics Education and Research for Knowledge-Circulating Society, ICKS 2008, pp. 20–25.

Linear algebra algorithms as dynamical systems

Acta Numerica, 17, 1–86.

Low-Dimensional Polytope Approximation and Its Applications to Nonnegative Matrix Factorization

Chu, M. T., & Lin, M. M. (2008, January 1). SIAM Journal on Scientific Computing, Vol. 30, pp. 1131–1155.

Model Order Reduction: Theory, Research Aspects and Applications

Schilders, W. H. A., Vorst, H. A., & Rommes, J. (2008, January 1). Mathematics in Industry.

Projected Pseudotransient Continuation

Kelley, C. T., Liao, L.-Z., Qi, L., Chu, M. T., Reese, J. P., & Winton, C. (2008, January 1). SIAM Journal on Numerical Analysis, Vol. 46, pp. 3071–3083.

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

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

Spectral decomposition of real symmetric quadratic $\lambda $-matrices and its applications

Chu, M. T., & Xu, S.-F. (2008, October 14). Mathematics of Computation, Vol. 78, pp. 293–313.

Spillover Phenomenon in Quadratic Model Updating

Chu, M. T., Datta, B., Lin, W.-W., & Xu, S. (2008, January 10). AIAA Journal, Vol. 46, pp. 420–428.

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

Chu, M. T., Buono, N. D., & Yu, B. (2007, January 1). SIAM Journal on Scientific Computing, Vol. 29, pp. 2668–2685.

Total decoupling of general quadratic pencils, Part I: Theory

Chu, M. T., & Buono, N. D. (2007, November 14). Journal of Sound and Vibration, Vol. 309, pp. 96–111.

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

Chu, M. T., & Buono, N. D. (2007, September 5). Journal of Sound and Vibration, Vol. 309, pp. 112–128.

Updating quadratic models with no spillover effect on unmeasured spectral data

Chu, M. T., Lin, W.-W., & Xu, S.-F. (2007, January 12). Inverse Problems, Vol. 23, pp. 243–256.

Low rank update of singular values

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

Reachable Matrices by a QR Step with Shift

Chu, D., & Chu, M. (2006, January 1). SIAM Journal on Applied Dynamical Systems, Vol. 5, pp. 91–107.

Inverse Eigenvalue Problems

Chu, M., & Golub, G. (2005, June 16). Oxford University Press EBooks, Vol. 9780198566649, pp. 1–406.

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 the Low-Rank Approximation of Data on the Unit Sphere

Chu, M., Buono, N. D., Lopez, L., & Politi, T. (2005, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 27, pp. 46–60.

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

Chu, M. T., Diele, F., & Ragni, S. (2005, October 10). Inverse Problems, Vol. 21, pp. 1879–1894.

Optimality, Computation and Interpretation of nonnegative matrix factorizations

[Preprint].

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

[Preprint].

On Inverse Quadratic Eigenvalue Problems with Partially Prescribed Eigenstructure

Chu, M. T., Kuo, Y.-C., & Lin, W.-W. (2004, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 25, pp. 995–1020.

On computing minimal realizable spectral radii of non-negative matrices

Chu, M. T., & Xu, S.-fang. (2004, July 7). Numerical Linear Algebra with Applications, Vol. 12, pp. 77–86.

On the least squares Euclidean distance matrix approximation and completion

[Preprint].

On the semigroup of standard symplectic matrices and its applications

Chu, M., Buono, N. D., Diele, F., Politi, T., & Ragni, S. (2004, June 8). Linear Algebra and Its Applications, Vol. 389, pp. 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].

Gradient flow methods for matrix completion with prescribed eigenvalues

Chu, M. T., Diele, F., & Sgura, I. (2003, April 4). Linear Algebra and Its Applications, Vol. 379, pp. 85–112.

On robust matrix completion with prescribed eigenvalues

Chu, M. T., Diele, F., & Sgura, I. (2003, September 16). Future Generation Computer Systems, Vol. 19, pp. 1139–1153.

Real-Valued, Low Rank, Circulant Approximation

Chu, M. T., & Plemmons, R. J. (2003, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 24, pp. 645–659.

Structured low rank approximation

Chu, M. T., Funderlic, R. E., & Plemmons, R. J. (2003, April 23). Linear Algebra and Its Applications, Vol. 366, pp. 157–172.

Structured inverse eigenvalue problems

Chu, M. T., & Golub, G. H. (2002, January 1). Acta Numerica, Vol. 11, pp. 1–71.

The Centroid Decomposition: Relationships between Discrete Variational Decompositions and SVDs

Chu, M. T., & Funderlic, R. E. (2002, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 23, pp. 1025–1044.

On the statistical meaning of truncated singular value decomposition

[Preprint].

The Orthogonally Constrained Regression Revisited

Chu, M. T., & Trendafilov, N. T. (2001, December 1). Journal of Computational and Graphical Statistics, Vol. 10, pp. 746–771.

A Fast Recursive Algorithm for Constructing Matrices with Prescribed Eigenvalues and Singular Values

Chu, M. T. (2000, January 1). SIAM Journal on Numerical Analysis, Vol. 37, pp. 1004–1020.

A mathematical framework for the linear reconstructor problem in adaptive optics

Chu, M. T., Pauca, V. P., Plemmons, R. J., & Sun, X. (2000, September 1). Linear Algebra and Its Applications, Vol. 316, pp. 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

Chu, M. T. (1999, February 1). Linear Algebra and Its Applications, Vol. 288, pp. 11–22.

A Numerical Method for the Inverse Stochastic Spectrum Problem

Chu, M. T., & Guo, Q. (1998, October 1). SIAM Journal on Matrix Analysis and Applications, Vol. 19, pp. 1027–1039.

Approximation by structured lower rank matrices

Chu, M. T., Funderlic, R. E., & Plemmons, R. J. (1998, October 2). Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE, Vol. 3461, pp. 268–279.

Cornelius Lanczos: Collected published papers with commentaries

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

Inverse Eigenvalue Problems

Chu, M. T. (1998, January 1). SIAM Review, Vol. 40, pp. 1–39.

On a differential equation approach to the weighted orthogonal Procrustes problem

MOODY, T. C. H. U., & TRENDAFILOV, N. I. C. K. O. L. A. Y. T. (1998, June 1). Statistics and Computing, Vol. 8, pp. 125–133.

On the Least Squares Approximation of Symmetric-Definite Pencils Subject to Generalized Spectral Constraints

Chu, M. T., & Guo, Q. (1998, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 19, pp. 1–20.

On the optimal consistent approximation to pairwise comparison matrices

Chu, M. T. (1998, March 1). Linear Algebra and Its Applications, Vol. 272, pp. 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

Chu, M. T., Funderlic, R. E., & Golub, G. H. (1998, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 20, pp. 428–436.

On a Variational Formulation of the Generalized Singular Value Decomposition

Chu, M. T., Funderlic, R. E., & Golub, G. H. (1997, October 1). SIAM Journal on Matrix Analysis and Applications, Vol. 18, pp. 1082–1092.

On the Least Squares Solution of Inverse Eigenvalue Problems

Chen, X., & Chu, M. T. (1996, December 1). SIAM Journal on Numerical Analysis, Vol. 33, pp. 2417–2430.

A Rank–One Reduction Formula and Its Applications to Matrix Factorizations

Chu, M. T., Funderlic, R. E., & Golub, G. H. (1995, December 1). SIAM Review, Vol. 37, pp. 512–530.

A list of matrix flows with applications

Hamiltonian and Gradient Flows, Algorithms and Control, 5, 87–97.

Constructing a Hermitian Matrix from Its Diagonal Entries and Eigenvalues

Chu, M. T. (1995, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 16, pp. 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].

Scaled Toda-like flows

Chu, M. T. (1995, January 1). Linear Algebra and Its Applications, Vol. 215, pp. 261–273.

The educational testing problem revisited

MOODY, T. C. H. U., & WRIGHT, J. O. E. L. W. (1995, January 1). IMA Journal of Numerical Analysis, Vol. 15, pp. 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

Chu, M. T., & Erbrecht, M. A. (1994, April 1). SIAM Journal on Matrix Analysis and Applications, Vol. 15, pp. 623–635.