An automatic multistep method for solving stiff initial value problems, J. Comput. Appl. Math., 9(1983), 229-238.

On a numerical treatment for the curve tracing of the homotopy method, Numer. Math., 42(1983), 323-329.

On the global convergence of the Toda lattice for real normal matrices and its applications to the eigenvalue problems, SIAM J. Math. Anal., 15(1984), 98-103.

The generalized Toda flow, the QR algorithm and the center manifold theorem, SIAM J. Alg. Disc. Meth., 5(1984), 187-210.

A simple application of the homotopy method to symmetric eigenvalue problems, Linear Alg. Appl., 59(1984), 85-90.

Asymptotic analysis of the Toda lattice on diagonalizable matrices, Nonlinear Anal. TMA, 9(1985), 193-201.

Symbolic calculation of the trace of the power of a tridiagonal matrix, Computing, 35(1985), 257-268.

A continuous approximation to the generalized Schur decomposition, Linear Alg. Appl., 78(1986), 119-132.

Continuous power method, preprint, 1986.

Curves on $S^{n-1}$ that lead to eigenvalues or their means of a matrix, SIAM J. Alg. Disc. Meth., 7(1986), 425-432.

On a differential equation approach to the singular value decomposition of bidiagonal matrices, Linear Alg. Appl., 80(1986), 71-79.

(with H. Hamilton), Parallel solution of ODE's by multiblock methods, SIAM J. Sci. Stat. Comput., 8(1987), 342-353.

(with H. Hamilton), Some remarks on the zero-stability of multiblock methods, preprint, 1987.

On a differential equation approach to the additive inverse eigenvalue problems, preprint, 1987.

A note on the homotopy method for linear algebraic eigenvalue problems, Linear Alg. Appl., 105(1988), 225-236.

On the continuous realization of iterative processes, SIAM Review, 30(1988), 375-387.

(with L. K. Norris), Isospectral flows and abstract matrix factorizations, SIAM J. Numer. Anal., 25(1988), 1383-1391.

(with T. Y. Li and T. Sauer), Homotopy method for general $\lambda$-matrix problems, SIAM J. Matrix Anal. Appl., 9(1988), 528-536.

(with G. H. Guirguis), A numerical method for the interface problem arising in the two-point boundary value problems, Computer methods in Applied Mechanics and Engineering, 74(1989), 99-113.

A derivative-free iterative method for locating the hand position of a robot manipulator, MCS-P48-0189, Argonne National Laboratory.

(with K. R. Driessel), Can real symmetric Toeplitz matrices have arbitrary real spectra? preprint, 1989.

(with K. R. Driessel), Some numerical experiments with isospectral flows, Technical Report 90-01, Idaho State University, 1990.

Solving additive inverse eigenvalue problems for symmetric matrices by the homotopy method, IMA J. Numer. Anal., 9(1990), 331-342.

(with K. R. Driessel), The projected gradient method for least squares matrix approximations with spectral constraints, SIAM J. Numer. Anal., 27(1990), 1050-1060.

A continuous Jacobi-like approach to the simultaneous reduction of real matrices, Linear Alg. Appl., 147(1991), 75-96.

Least squares approximation by real normal matrices with specified spectrum, SIAM J. Matrix Anal. Appl., 12(1991), 115-127.

(with K. R. Driessel), Constructing symmetric nonnegative matrices with prescribed eigenvalues by differential equations, SIAM J. Math. Anal., 22(1991), 1372-1387.

Matrix differential equations: A continuous realization process for linear algebra problems, Nonlinear Anal., TMA, 18(1992), 1125-1146.

Numerical methods for inverse singular value problems, SIAM J. Numer. Anal., 29(1992), 885-903.

On the inverse eigenvalue problem for real circulant matrices, preprint, 1992.

On the differential equation $\frac{dX}{dt} = [X,k(X)]$ where $k$ is a Toeplitz annihilator, preprint, 1993.

(with J. L. Watterson), On a multivariate eigenvalue problem: I. Algebraic Theory and Power method, SIAM J. Sci. Comput., 14(1993), 1089-1106.

The stability group of symmetric Toeplitz matrices, Linear Alg. Appl., 185(1993), 119-123.

(with M. A. Erbrecht), Symmetric Toeplitz matrices with two prescribed eigenpairs, SIAM J. Matrix Anal. Appl., 15(1994), 623-635.

A list of matrix flows with applications, Proceedings of Workshop on Hamiltonian and Gradient Flows, Algorithms and Control, Fields Institute, Canada, 1992, Fields Institute Communications, 3(1994), 87-97.

Scaled Toda-like flows, Linear Alg. Appl., 215(1995), 261-273.

(with J. W. Wright), Educational testing problem and non-smooth optimization, IMA J. Numer. Anal., 15(1995), 141-160.

Constructing a Hermitian Matrix from Its Diagonal Entries and Eigenvalues, SIAM J. Matrix Appl., 16(1995), 207-217.

(with R. E. Funderlic and G. H. Golub), A rank-one reduction formula and its relations to other matrix factorizations, SIAM Review, 37(1995), 512-530; also Manuscript SCCM-94-07, Stanford University, 1994.

(with X. Chen), On the least squares solution of inverse eigenvalue problems, SIAM J. Numer. Anal., 33(1996), 2417-2430.

(with R. E. Funderlic and G. H. Golub), On a new geometric meaning of the BFGS update, preprint, 1995.

On the refinement of a Newton method for the inverse Toeplitz eigenvalue Problem, preprint, 1995.

(with R. E. Funderlic and G. H. Golub), On a variational formulation of the generalized singular value decomposition, SIAM J. Matrix Anal. Appl., 18(1997), 1082-1092.

(with Q. Guo), On the least squares approximation of symmetric-definite pencils subject to generalized spectral constraints, SIAM J. Matrix Anal. Appl., 19(1998), 1-20.

Inverse eigenvalue problems, SIAM Review, 40(1998), 1-39.

(with Q. Guo), A numerical method for the inverse stochastic spectrum problem, SIAM J. Matrix Anal. Appl., 19(1998), 1027-1039.

(with R. E. Funderlic and G. H. Golub), Rank modifications of semi-definite matrices with applications to secant updates, SIAM J. Matrix Anal. Appl., 20(1998), 428-436.

(with R. Plemmons), Numerical methods for adaptive-optics systems, preprint, 1995.

(with N. T. Trendafilov), The orthogonally constrained regression revisited, J. Comput. Graph. Stat., 10(2001), 746-771.

(with N. T. Trendafilov), On a differential equation approach to the weighted orthogonal Procrustes problem, Statistics \& Computing, 8(1998), 125-133.

(with N. T. Trendafilov), ORTHOMAX rotation problem: a differential equation approach, Behavirometrika, 25(1998), 13-23.

On the optimal consistent approximation to pairwise comparison matrices, Linear Alg. Appl., 272(1998), 155-168.

(with R. E. Funderlic and R. J. Plemmons) Approximation by structured lower rank matrices, Proceedings of SPIE, in Advanced Signal Processing, Algorithm, Architectures, and Implementations, VIII, 3461(1998), 268-279.

On constructing matrices with prescribed singular values and diagonal elements, Linear Alg. Appl., 288(1999), 11-22.

(with N. T. Trendafilov), A continuous-time approach to the oblique Procrustes problem, Behavirometrika, 26(1999), 167-181.

A fast recursive algorithm for constructing matrices with prescribed eigenvalues and singular values, SIAM J. Numer. Anal., 37(2000), 1004-1020.

(with V. P. Pauca, R. J. Plemmons, and X. Sun), A mathematical framework for the linear reconstructor problem in adaptive optics, Linear Alg. Appl., 316(2000), 113-135.

On an adaptive control algorithm for the adaptive optics problems, preprint, 1999.

(with R. E. Funderlic), The Centroid Decomposition: Relationships between Discrete Variational Decompositions and SVD, SIAM J. Mat. Anal. Appl., 23(2001), 1025-1044.

(with G. Golub), Structured Inverse Eigenvalue Problems, Acta Numerica, invited paper, 2002, 1-71.

(with R. E. Funderlic and R. J. Plemmons), Structured low rank approximation, Linear Alg. Appl., 366(2003), 157-172.

(with R. J. Plemmons), Real-valued, low rank circulant approximation, SIAM J. Mat. Anal. Appl., 24(2003), 645-659.

On the statistical meaning of truncated singular value decomposition, preprint, 2001.

(with F. Diele and I. Sgura), Gradient flow methods for matrix completion with prescribed eigenvalues, Linear Alg. Appl., 379(2004), 85-112.

(with F. Diele and I. Sgura), On the robust matrix completion with prescribed eigenvalues, Future Generation Computing Systems, 19(2003), 1139-1153.

(with Y. C. Kuo and W. W. Lin), On inverse quadratic eigenvalue problems with partially prescribed eigenstructure, SIAM J. Mat. Anal. Appl., 25(2004), 995-1020.

(with Y. C. Kuo and W. W. Lin), On the existence and uniqueness of a solution to the inverse monic quadratic eigenvalue problem, SIAM J. Mat. Anal. Appl., 25(2004), 995-1020.

(with D. I. Chu and H. Brown), On the least squares Euclidean distance matrix approximation and completion, Optimization and Engineering, submitted, 2004.

(with S. F. Xu), On computing minimal realizable spectral radii of nonnegative matrices, J. Numer. Linear Alg. Appl., 12( 2005), 77-86..

(with N. Del Buono, F. Diele, T. Politi, and S. Ragni), On the semigroup of standard symplectic matrices and its applications, Linear Alg. Appl., 389(2004), 215-225.

(with N. Del Buono, L. Lopez, and T. Politi), On the low rank approximation of data on the unit sphere, SIAM J. Mat. Anal. Appl., 27(2005), 46-60. (DOI: 10.1137/S0895479803433295)

Group theory, linear transformations, and flows: Dynamical systems on manifolds, Preprint, 2004.

(with N. Orlowski, D. Schlorff, J. Blevins, D. Canas, and R. Funderlic), The effect of ties on convergence in the $k$-modes variants for clustering categorical data, Preprint, 2004.

(with F. Diele, R. Plemmons, and S. Ragni), Optimality, Computation and Interpretation of nonnegative matrix factorizations, Preprint, 2005.

(with R. Plemmons), Nonnegative matrix factorization and applications, IMAGE, 34(2005), 1-5.

(with F. Diele and S. Ragni), On the inverse problem of constructing symmetric pentadiagonal Toeplitz matrices from three largest eigenvalues, Inverse Problems, 21(2005), 1879-1894.

(with D. Chu), Singular value reassignment with low rank matrices, Math. Comput.,75(2006), 1351-1366.

(with D. Chu), Reachable set by the QR iteration with shifts, SIAM J. Applied Dynamical Systems, 5(2006), 91-107.

(with S. Ragni, C. Marangi, andF. Diele) Estimating the consumption matrix from inexact data in the Leontief model, J. Numer. Anal. Indus. Appl. Math., 2(2007), 139-156.

(with N. Del Buono and B. Yu), Structured quadratic inverse eigenvalue problem, I. Serially linked systems, SIAM J. Sci. Comput, 29(2007), 2668-2685. (DOI: 10.1137/060672510)

(with W.-W. Lin and S.-F. Xu), Updating quadratic models with no spill-over effect on unmeasured spectral data, Inverse Problems, 23(2007), 243-256.

(with N. Del Buono), Total decoupling of general quadratic pencils, Part I: Theory, J. Sound Vibration, 309(2008), 96-111. (DOI: 10.1016/j.jsv.2007.05.058)

(with N. Del Buono), Total decoupling of general quadrtic pencils, Part II: Structure preserving isospectral flows, J. Sound and Vibration, 309(2008), 112-128. (DOI: 10.1016/j.jsv.2007.05.052)

Quadratic inverse eigenvalue problems and its applications to model updating an overview, in Model Order Reduction: Theory, Research Aspects and Applications, (Eds.) Wilhemlus Schilders, Henk van der Vorst, Joost Rommes, Springer, ISBN: 978-3-540-78840-9, Lorenz Center, Leiden University, 271-290, 2008..

(with B. Datta, W.-W. Lin and S.-F. Xu), The spill-over phenomenon in quadratic model updating, AIAA J., 46(2008), 420-428.

(with M. M. Lin), Low dimensional polytope approximation and its applications to nonnegative matrix factorization, SIAM J. Sci. Comput., 30(2008), 1131-1151..

(with C. T. Kelley, L.-Z. Liao, L.-Q. Qi, J. P. Reese and C. Winton), Projected pseudo-transient continuation, SIAM J. Numer. Ana., 46(2008), 3071-3083.

(with S. Xu), Spectral decomposition of real symmetric quadratic $\lambda $-matrices and its applications, Math. Comput., 78(2009), 293-313.

(with D. Chu and W.-W. Lin), Real symmetric quadratic model updating that preserves positive definiteness and no spill-over, SIMAX J. Mat. Anal. Appl., 31(2009), 546-564.

Data mining and applied linear algebra, International Conference on Informatics Education and Research for Knowledge-Circulating Society, ICKS 2008, 20-25.

Numerical linear algebra algorithms as dynamical systems, Acta Numerica, 17(2008), 1-86.

(with B. Dong and M. Lin), Parameter reconstruction of vibration systems from partial eigeninformation, Journal of Sound and Vibration, 327(2009), 391-401.

(with M. Lin and B. Dong), Inverse mode problem for real symmetric quadratic models, Inverse Problems, 26(2010), 065003, (DOI: 10.1088/0266-5611/26/6/065003)

(with M. Lin and B. Dong), Semi-definite programming techniques for structured quadratic inverse eigenvalue problems, Numer. Algorithms, 53(2010), 419-437.

(with M. Lin and B. Dong), Integer matrix factorization and its applications, Preprint, 2009.

(with M. Lin), On the nonnegative rank of Euclidean distance matrices, Linear Alg. Appl., 433(2010), 681-689.

On the nonnegative rank of Euclidean distance matrices, II, preprint, 2010.

(with M. Lin), Dynamical System Characterization of the Central Path and Its Variants --- A Revisit, SIAM. J. Appl. Dyn. Syst. 10(2011), 887-905.

(with L.-H. Zhang), Computing absolute maximum correlation, IMA J. Numer. Anal., 32(2012), 163-184.

(with C.-H. Kuo and M. Lin), Spline Approximation of policy functions in Economics with Uncertainties, Computational Economics, 42(2013), 175-198, (DOI: 10.1007/s10614-012 9331-1)

(with M. Lin and L. Wang), A study of the singular spectrum analysis with the global optimization techniques, J. Global Optimization, (DOI:10.1007/s10898-013-0117-3), J. Global Optim. 60 (2014), no. 3, 551574.

(with M. Lin and B. Dong), Nonnegative rank factorization a heuristic approach via rank reduction, Numer. Algorithms, 65(2014), 251-274, (DOI: 10.1007/s11075-013-9704-0).

(with M. Lin), On the finite rank and finite dimensional representation of bounded semi-infinite hankel operators, IMA J. Numer. Anal., (DOI: 10.1093/imanum/dru001), 2014.

(with L. Wang), On the global convergence of the alternating least method for rank-one approximation to generic tensors, SIAM J. Matrix Ana. Appl., 35(2014), 1058-1072.

(with L. Wang and B. Yu), Orthogonal low-rank tensor approximation: Alternating least square method and its global convergence, SIAM J. Matrix Ana. Appl., 36(2015), 1-19.

(with S.-J. Wu), Attaining the optimal Gaussian diffusion acceleration, J. Stat. Phys., 155(2014), 571-590.

(with L. Wang and B. Yu), Gradient flow for generalized normal equation with applications to linear matrix equations, 68(2015), 121-141, Numer. Algorithms, (DOI:10.1007/s11075-014-9885-1).

(with S.-J. Wu), On the second dominant eigenvalue affecting the power method for transition probability tensors, Preprint, 2014.

(with S.-J. Wu), Constructing optimal transition matrix for Markov Chain Monte Carlo via Global Optimization, Linear Alg. Appl., 487(2015), 184-202.

Solving Nonlinear Matrix Equation $X+A^{*}X^{-1}A = Q$ Fej\'{e}r-Riesz Factorization, Linear Alg. Appl., 489(2016), 123-143.

(with Z. Zhang), An Innate Moving Frame on Parametric Surfaces: The Dynamics of Principal Singular Curves, Preprint, 2016.

On the dynamics of maximin flows, Preprint, 2016.

(with S.-J. Wu), Markov Chains with Memory, Tensor Formulation, and the Dynamics of Power Iteration, Applied Math. Comput., 303(2017), 226-239.

(with S.-J. Wu), Solving an inverse eigenvalue problem subject to triple constraints on diagonal elements, eigenvalues, and singular values, Inverse Problems, 33(2017), no. 8, 085003.

(with Y. Guan and D. Chu) SVD-based algorithms for the best rank-1 approximation of a symmetric tensor, SIAM J. Matrix Anal. Appl., to appear.

On the adjoint of tensors, Preprint, 2017.

(with L.Z. Liao) Numerical methods for gradient dynamics, Preprint, submitted, 2017.

(with Y. Guan) Convergence analysis of an SVD-based algorithm for the best rank-1 tensor approximation, submitted, 2017.