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
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(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
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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
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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),
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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, 551–574.

(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, Preprint, submitted, 2017.

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, preprint, 2017.