- An automatic multistep
method for solving stiff initial value problems,
J. Comput. Appl.
Math., 9(1983), 229-238.
(abstract) (postscript) (pdf)
- On a numerical treatment
for the curve tracing of the homotopy method,
Numer. Math.,
42(1983), 323-329.
(abstract) (postscript) (pdf)
- 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.
(abstract) (postscript) (pdf)
- 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.
(abstract) (postscript) (pdf)
- Asymptotic analysis of the
Toda lattice on diagonalizable matrices,
Nonlinear Anal. TMA, 9(1985), 193-201.
(abstract) (postscript) (pdf)
- 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.
(abstract) (postscript) (pdf)
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.
(abstract) (postscript) (pdf)
- (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.
(abstract) (postscript) (pdf)
- On the continuous
realization of iterative processes,
SIAM
Review, 30(1988), 375-387.
(abstract) (postscript) (pdf)
- (with
L. K. Norris), Isospectral
flows and abstract matrix factorizations,
SIAM
J. Numer. Anal., 25(1988), 1383-1391.
(abstract) (postscript) (pdf)
- (with
T. Y. Li and T. Sauer), Homotopy
method for general $\lambda$-matrix problems,
SIAM
J. Matrix Anal. Appl., 9(1988), 528-536.
(abstract) (postscript) (pdf)
- (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.
(abstract) (postscript) (pdf)
- A derivative-free
iterative method for locating the hand position of a robot manipulator,
MCS-P48-0189,
Argonne National Laboratory.
(abstract) (postscript)
(pdf)
- (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.
(abstract) (postscript)
(pdf)
- A continuous Jacobi-like
approach to the simultaneous reduction of real matrices,
Linear Alg. Appl., 147(1991), 75-96.
(abstract) (postscript)
(pdf)
- Least squares
approximation by real normal matrices with specified spectrum,
SIAM J. Matrix Anal. Appl.,
12(1991), 115-127.
(abstract) (postscript)
(pdf)
- (with
K. R. Driessel), Constructing
symmetric nonnegative matrices with prescribed eigenvalues by differential
equations,
SIAM J. Math. Anal., 22(1991),
1372-1387.
(abstract) (postscript)
(pdf)
- Matrix differential
equations: A continuous realization process for linear algebra problems,
Nonlinear Anal.,
TMA, 18(1992), 1125-1146.
(abstract) (postscript)
(pdf)
- Numerical methods for
inverse singular value problems,
SIAM J. Numer. Anal., 29(1992),
885-903.
(abstract) (postscript)
(pdf)
- On the inverse eigenvalue
problem for real circulant matrices,
preprint, 1992.
(abstract) (postscript)
(pdf)
- On the differential
equation $\frac{dX}{dt} = [X,k(X)]$ where $k$ is a Toeplitz annihilator,
preprint, 1993.
(abstract) (postscript)
(pdf)
- (with
J. L. Watterson), On
a multivariate eigenvalue problem: I. Algebraic Theory and Power
method,
SIAM J. Sci. Comput., 14(1993),
1089-1106.
(abstract) (postscript)
(pdf)
- The stability group of
symmetric Toeplitz matrices,
Linear Alg. Appl., 185(1993), 119-123.
(abstract) (postscript)
(pdf)
- (with
M. A. Erbrecht), Symmetric
Toeplitz matrices with two prescribed eigenpairs,
SIAM
J. Matrix Anal. Appl., 15(1994), 623-635.
(abstract) (postscript)
(pdf)
- 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.
(abstract) (postscript)
(pdf)
Linear Alg.
Appl., 215(1995), 261-273.
(abstract) (postscript)
(pdf)
- (with
J. W. Wright), Educational
testing problem and non-smooth optimization,
IMA
J. Numer. Anal., 15(1995), 141-160.
(abstract) (postscript)
(pdf)
- Constructing a Hermitian
Matrix from Its Diagonal Entries and Eigenvalues,
SIAM
J. Matrix Appl., 16(1995), 207-217.
(abstract) (postscript)
(pdf)
- (with
R. E. Funderlic and G. H. Golub), A
rank-one reduction formula and its relations to other matrix
factorizations,
Manuscript SCCM-94-07, Stanford University, 1994; also SIAM Review,
37(1995), 512-530.
(abstract) (postscript)
(pdf)
- (with
X. Chen), On the
least squares solution of inverse eigenvalue problems,
SIAM J. Numer. Anal., 33(1996),
2417-2430.
(abstract) (postscript)
(pdf)
- (with
R. E. Funderlic and G. H. Golub), On
a new geometric meaning of the BFGS update,
preprint, 1995.
(abstract) (postscript)
(pdf)
- On the refinement of a Newton method for the
inverse Toeplitz eigenvalue Problem,
preprint, 1995.
(abstract) (postscript)
(pdf)
- (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.
(abstract) (postscript)
(pdf)
- (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.
(abstract) (postscript)
(pdf)
- Inverse eigenvalue
problems,
SIAM
Review, 40(1998), 1-39.
(abstract) (postscript)
(pdf)
- (with
Q. Guo), A numerical
method for the inverse stochastic spectrum problem,
SIAM
J. Matrix Anal. Appl., 19(1998), 1027-1039.
(abstract) (postscript)
(pdf)
- (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.
(abstract)
(postscript) (pdf)
- (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.
(abstract) (postscript)
(pdf)
- (with
N. T. Trendafilov), On
a differential equation approach to the weighted orthogonal Procrustes
problem,
Statistics
\& Computing, 8(1998), 125-133.
(abstract) (postscript)
(pdf)
- (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.
(abstract) (postscript)
(pdf)
- (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.
(abstract) (postscript)
(pdf)
- (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.
(abstract) (postscript)
(pdf)
- (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.
(abstract) (postscript)
(pdf)
- On an adaptive control
algorithm for the adpative optics problems,
preprint, 1999.
(abstract) (postscript)
(pdf)
- (with
R. E. Funderlic), The
Centroid Decomposition: Relationships between Discrete Variational
Decompositions and SVD,
SIAM J. Mat. Anal. Appl., 23(2001),
1025-1044.
(abstract) (postscript)
(pdf)
- (with
G. Golub), Structured
Inverse Eigenvalue Problems,
Acta Numerica,
invited paper, 2002, 1-71.
(abstract) (postscript)
(pdf)
- (with
R. E. Funderlic and R. J. Plemmons), Structured
low rank approximation,
Linear Alg.
Appl., 366(2003), 157-172.
(abstract) (postscript)
(pdf)
- (with
R. J. Plemmons) Real-valued,
low rank circulant approximation,
SIAM
J. Mat. Anal. Appl., 24(2003), 645-659.
(abstract) (postscript)
(pdf)
- On the statistical meaning
of truncated singular value decomposition,
preprint, 2001.
(abstract) (postscript)
(pdf)
- (with
F. Diele and I. Sgura) Gradient flow methods for
matrix completion with prescribed eigenvalues,
Linear Alg.
Appl., 379(2004), 85-112.
(abstract) (postscript)
(pdf)
- (with
F. Diele and I. Sgura) On the robust matrix
completion with prescribed eigenvalues,
Future
Generation Computing Systems, 19(2003), 1139-1153.
(abstract) (postscript)
(pdf)
- (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.
(abstract) (postscript)
(pdf)
- (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.
(abstract) (postscript)
(pdf)
- (with D. I.
Chu and H. Brown) On the least squares Euclidean distance
matrix approximation and completion,
Optimization and Engineering,
submitted, 2004.
(abstract) (postscript)
(pdf)
- (with
S. F. Xu) On
computing minimal realizable spectral radii of nonnegative matrices,
J. Numer. Linear Alg. Appl., 12( 2005), 77-86..
(abstract) (postscript)
(pdf)
- (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.
(abstract) (postscript) (pdf)
- (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..
(abstract) (postscript)
(pdf)
(DOI:
10.1137/S0895479803433295)
- Group theory, linear
transformations, and flows: Dynamical systems on manifolds,
Preprint, 2004.
(abstract) (postscript)
(pdf)
- (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.
(abstract) (postscript)
(pdf)
- (with
F. Diele, R. Plemmons, and S. Ragni) Optimality,
Computation and Interpretation of nonnegative matrix factorizations,
Preprint, 2005.
(abstract) (postscript)
(pdf)
- (with
R. Plemmons) Nonnegative matrix
factorization and applications,
IMAGE, 34(2005),
1-5.
(abstract) (postscript)
(pdf)
- (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.
(abstract) (postscript) (pdf)
- (with
D. Chu) Singular
value reassignment with low rank matrices,
Math.
Comput.,75(2006), 1351-1366.
(abstract) (postscript)
(pdf)
- (with
D. Chu) Reachable set by the QR iteration with shifts,
SIAM
J. Applied Dynamical Systems, 5(2006), 91-107.
(abstract) (postscript)
(pdf)
- (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.
(abstract) (postscript) (pdf)
- (with
N. Del Buono and B. Yu) Structured
quadratic inverse eigenvalue problem, I. Serially linked systems,
SIAM
J. Sci. Comput, 29(2007), 2668-2685.
(abstract)(postscript)(pdf)
(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.
(abstract)(postscript)(pdf)
- (with
N. Del Buono) Total decoupling of general quadratic
pencils, Part I: Theory,
J. Sound
Vibration, 309(2008), 96-111.
(abstract) (postscript) (pdf)
(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.
(abstract) (postscript) (pdf)
(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..
(abstract)(postscript)(pdf)
- (with
B. Datta, W.-W. Lin and S.-F. Xu) The
spill-over phenomenon in quadratic model updating,
AIAA J.,
46(2008), 420-428.
(abstract)(postscript)(pdf)
- (with
M. M. Lin) Low
dimensional polytope approximation and its applications to nonnegative
matrix factorization,
SIAM
J. Sci. Comput., 30(2008), 1131-1151..
(abstract)(postscript)(pdf)
- (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..
(abstract)(postscript)(pdf)
- (with S. Xu) Spectral
decomposition of real symmetric quadratic $\lambda $-matrices and its
applications,
Math. Comput.,
78(2009) 293-313.
(abstract)(postscript)(pdf)
- (with
D. Chu and W.-W. Lin) Real
symmetric quadratic model updating
that preserves positive definiteness and no spill-over,
To appear, SIMAX J. Mat. Anal.
Appl., 2008.
(abstract)(postscript)(pdf)
- Data mining and applied linear
algebra,
International
Conference on Informatics Education and Research for Knowledge-Circulating
Society,
ICKS 2008, 20-25.
(abstract)(postscript)(pdf)
- Numerical linear algebra
algorithms as dynamical systems,
Acta Numerica, 17(2008), 1-86.
(abstract)(postscript)(pdf)
- (with
B. Dong and M. Lin) Parameter
reconstruction of vibration systems from partial eigeninformation,
Journal of Sound
and Vibration, 327(2009), 391-401.
(abstract)(postscript)(pdf)
- (with
B. Dong and M. Lin) Nonnegative
rank factorization via rank reduction,
Preprint, 2008.
(abstract)(postscript)(pdf)
- (with
L.-H. Zhang) On a Multivariate Eigenvalue
Problem: II. Global solutions and the Gauss-Seidel Method,
Preprint, 2008.
(abstract)(postscript)(pdf)
- (with
M. Lin and B. Dong) Inverse mode problem for real symmetric
quadratic models,
Preprint, 2009.
(abstract)(postscript)(pdf)
- (with
M. Lin and B. Dong) Semi-definite
programming techniques for structured quadratic inverse eigenvalue
problems,
Numerical Algorithms, to appear,
2009.
(abstract)(postscript)(pdf)
- (with
M. Lin and B. Dong) Integer matrix factorization and its
applications,
Preprint, 2009.
(abstract)(postscript)(pdf)
- (with
M. Lin) On the nonnegative rank of Euclidean distance
matrices,
Preprint, 2009.
(abstract)(postscript)(pdf)