Papers reviewed by Math. Review is listed in MathSciNet.
- Orthogonal Recurrent Neural Networks with Scaled Cayley Transform, (with K. Helfrich and D. Willmott), arXiv:1705.09520 [stat.ML], Proceedings of the 35th International Conference on Machine Learning
( ICML 2018), PMLR 80:1974-1983, 2018.
- State inference of RNA secondary structures with deep recurrent neural networks
, (with D. Willmott and D. Murrugarra), ( Preprint.)
- Preconditioning for Accurate Solutions of Linear Systems and Eigenvalue Problems, Preprint available at arXiv:1705.04340 [math.NA].
- Error Bounds for the Krylov Subspace methods for Computations of Matrix Exponentials, (with H. Wang), ( arXiv:1603.07358 [math.NA]), SIAM J. Matrix Anal. Appl., 38(1), 155187.
- Accurate inverses for computing eigenvalues of extremely ill-conditioned matrices and differential operators, arXiv:1512.05292 [math.NA],
Math. Comp. 87 (2018), 237-259
- Deflation by restriction for the inverse-free
preconditioned Krylov subspace method , (with Q. Liang), Numerical Algebra, Control and Optimization, 6(2016): 55 - 71.
- Outlier Detection in the Framework of Dimensionality Reduction , (with W. Zhi), Int. J. Patt. Recogn. Artif. Intell. , 29 (2015):1550017 [19 pages].
- Discrete Hessian Eigenmap Algorithm for Dimensionality Reduction , (with W. Zhi), J. Comp. Applied Math., 278(2015):197212.
Computing Singular Values of Large Matrices With Inverse Free Preconditioned Krylov Subspace Method
, (with Q. Liang), Electron. Trans. Numer. Anal.,, 42(2014):197-221.
- Relative perturbation theory for diagonally dominant matrices, (with M. Dailey and F. M. Dopico), SIAM J. Matrix Anal. Appl.,, 35(2014), 13031328.
- New relative perturbation bounds for LDU factorizations of diagonally dominant matrices, (with M. Dailey and F. M. Dopico), SIAM J. Matrix Anal. Appl.,, 35(2014), 904930.
- Simultaneous Similarity Reductions for a Pair of Matrices to Condensed Forms (with R.C. Li), Comm. Math. Statis., 2(2014):139-153.
- Computing Exponentials of Essentially Non-negative Matrices Entrywise to High Relative Accuracy (with J. Xue), Math. Comp.,, 82 (2013), 1577-1596.
- Analysis of Alignment Algorithms with Mixed Dimensions for Dimensionality Reduction,
(with W. Zhi)
Numer. Linear Algebra Appl., 20(2013):369-384.
- Error Bounds for the Lanczos Methods for Approximating Matrix Exponentials, SIAM J. Numer. Anal. 51(2013), 6887
- Infinite matrices bounded on weighted L1 spaces, (with J. Williams) Linear Algebra Appl. 438 (2013), no. 12, 46894700.
- Eigenvalue Bounds for an Alignment Matrix in Manifold
Learning (with W. Zhi), Linear Algebra and its Applications, 436(2012):29442962.
- Tikhonov regularization based on
generalized Krylov subspace methods (with L. Reichel and F. Sgallari),
Applied Numerical Mathematics 62 (2012) : 12151228
- Inexact Subspace Iterations For the Generalized Eigenvalue Problems (with P. Zhang),
Linear Algebra and its Applications,
- Alignments of Manifold Sections of Different
Dimensions in Manifold Learning, (with W. Zhi), Proceedings of
AAAI Fall 2010 Symposium on Manifold Learning and Its Applications,
November, 2010, Arlington, VA, vol. 6, pp.63-68.
- A Block Inverse-free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems (with P. Quillen),
J. Comp. Applied Math 233(2010):1298-1313
- Relative Perturbation Bounds for Eigenvalues of Diagonally Dominant Matrices,
SIAM J. Matrix Anal. Appl. 31(2009):11-17.
- Simple square smoothing regularization operators (with L. Reichel)
Electron. Trans. Numer. Anal. 33 (2008/09), 6383.
- Entrywise Relative Perturbation Bounds for
Exponentials of Essentially Nonnegative Matrices, (with J. Xue), Numer. Math. 110(2008):393--403.
Singular Values of Diagonally Dominant Matrices to High Relative Accuracy, Math. Comp. 77(2008), 2195-2230. (Erratum for Theorem 3 in the case of the column diagonal dominance pivoting.)
Generalized LSQR Algorithm, (with L. Reichel), Numer. Linear Algebra Appl. 15(2008) : 643-660.
Expansion of Subspaces for Eigenvector Approximations, Linear
Algebra Appl. 428(2008):
- Analysis of an Algnment
Algorithm for Nonlinear Dimensionality Reduction (with H. Zha, R.C. Li), BIT
- Numerical Mathematics, 47,
- Eigenvalues of An
Alignment Matrix in Nonlinear Manifold Learning, (with C. Li, R.C. Li), Comm. Math. Sciences, 5(2007):313-329.
the Uniqueness of Surface Wave Inversion Using Multiple-Mode Dispersion
Data, (with Y. Supranata, M. Kalinski),
International Journal of Geomechanics 7
- Krylov type subspace methods for matrix polynomials,
(with L. Hoffnung and R.C. Li ), Linear
Algebra Appl., 415
Iterated Shift-and-invert Arnoldi Algorithm for Quadratic
Matrix Eigenvalue Problems, Applied
Math. Comp. 172(2006):818-827.
845: EIGIFP: A MATLAB Program for Solving Large Symmetric Generalized Eigenvalue Problems, (with James Money), ACM
Transaction on Mathematical Softwares, 31(2005):270-279.
GMRES for Singular Systems, (with L. Reichel),
J. Matrix Anal. Appl., 26(2005):1001 1021.
- A Krylov subspace method for quadratic matrix polynomials
with application to constrained
least squares problems, (with R.C. Li), SIAM
J. Matrix Analysis Appl., 25 (2003):405-428.
inverse free preconditioned krylov
subspace method for symmetric generalized eigenvalue
problems (with G.
J. Sci. Comp. 24 (2002):312-334.
- Entrywise perturbation theory for diagonally dominant
M-matrices with applications, (with A. Alfa, J. Xue),
Numer. Math. 90
computation for the smallest eigenvalue of a diagonally
dominant M-matrices, (with A. Alfa, J. Xue),
Comp. 71 (2002):217-236.
Estimate of Spectral Radii of Rate Matrices of GI/M/1 Type Markov
Chains, Matrix-Analytic Methods,
Theory and Applications , G. Latouche and
P.G. Taylor (Editors), 2002, World Scientific, NJ. pp. 403-416.
- On Latouche-Ramaswami's Logarithmic Reduction Algorithm
for Quasi-birth-and-death Processes, Stoch. Models, 18 (2002):449-467. (Awarded the
Marcel F. Neuts Prize.)
Inverse Iterations for the Generalized Eigenvalue
Problems, (with G.
- Numerical Mathematics,
40 (2000): 672-684.
theory for the asymptotic decay rates in the
queues with Markovian arrival process,
(with A. Alfa, J.Xue), Queueing Systems - Theory and Applications 36 (2000):287-301.
accuracy algorithms for solving nonlinear matrix equations in queueing models, Advances in Algorithmic Methods for
Stochastic Models - Proceedings
of the 3rd International Conference on Matrix Analytic Methods, G. Latouche and P.G. Taylor (Editors), 2000,
Notable Publications Inc. NJ. pp. 401-415.
- Entrywise perturbation theory for rate matrices of
GI/M/1 type Markov chains, (with A. Alfa, J. Xue), Stoch. Models 16
Replacement Strategies for Krylov Subspace
Iterative Methods for the Convergence of True Residuals, (with H. van der
J. Sci. Comp. 22 (2000):836-852.
preconditioned conjugate gradient method with inner-outer iteration,
J. Sci. Comp. 21 (2000):1305-1320.
of finite precision bi-conjugate gradient algorithm for nonsymmetric linear systems, (with Charles Tong), Math. Comp. 69 (2000):1559-1575.
analysis of groundwater flow in an infinite region with a sinusoidal top,
(with P.N. Shivakumar,
J.J. Williams, C. Ji),
Numer. Funct. Anal. Optim. 21 (2000):263-271.
- ABLE: an
Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems, (with Z. Bai and
D. Day), SIAM
J. Matrix Anal. Appl. 20
- A variational principle for eigenvalues
of pencils of Hermitian matrices, (with P. Binding, B. Najman), Integral
Equations and Operator Theory, 35 (1999): 398-422.
Bound for Reduced System Model by Pade
Approximation Via the Lanczos Process,
(with Z. Bai,
R. Slone, W. Smith), IEEE
Trans. on Computer-Aided Design 18
Estimation of the Pade Approximation of Transfer
Functions Via the Lanczos Process, (with Z.
Bai), Electronic Transaction of Numerical
Analysis, 7 (1998):1-17.
Mixed Product Krylov Subspace method for Solving
Nonsymmetric Linear Systems, (with T. F. Chan), Asian J. Math. 1 (1997):422-434.
linear system solver based on a modified Krylov
subspace method for breakdown recovery, (with Charles Tong), Numer. Alg. 12
two-sided bounds related to weakly diagonally dominant M-matrices with
applications to digital circuit dynamics, (with P.N. Shivakumar,
J.J. Williams, C. Marinov), SIAM
J. Matrix Anal. Appl. 17(1996):298-312.
for the width of the instability intervals in the Mathieu equation,
Shivakumar), Operator Theory: Advances and
Applications vol.87, Birkhauser, Basel, 1996, pp. 348
adaptive block Lanczos algorithm, Numer. Alg. 12
- On close eigenvalues
of tridiagonal matrices, Numer. Math. 70
- Variational principles for indefinite eigenvalue problems, (with P.A. Bining),
Algebra Appl. 218 (1995):251-262
breakdown-free variation of the nonsymmetric Lanczos algorithms, Math. Comp. 62 (1994):179-207.
rank perturbations of strongly definitizable
transformations and matrix polynomials, (with
P. Lancaster, A.
Algebra and Appl. 198 (1994):3-29.
definitizable linear pencils in Hilbert space, (with P. Lancaster, A. Shkalikov), Integral
Equations Operator Theory, 17 (1993):338-360.
and Lanczos methods for symmetric matrix
pencils, (with P.
Algebra Appl. 185 (1993):173-201.
- Definitizable hermitian
matrix pencils, (with P. Lancaster), Aequationes Mathematicae 46
- A minimax characterization for eigenvalues
of Hermitian pencils II (with B. Najman), Linear
Algebra Appl. 191 (1993):183-197.
general variational principles, (with P. A.
Binding), Proc. Amer. Math. Soc. 114 (1992):107-114
convergence analysis of nonsymmetric Lanczos algorithms, Math. Comp. 56 (1991):677-691.
- Variational principles without definiteness
conditions, (with P. Binding), SIAM
J. Math. Anal. 22 (1991):1575-1583
- A minimax characterization for eigenvalues
of hermitian pencils, (with B. Najman), Linear
Alg. Appl. 144 (1991):217-230
- Variational and numerical methods for symmetric matrix
pencils, (with P. Lancaster), Bulletin of Austr. Math. Soc. 43(1991):1-17
- Variational properties and Rayleigh quotient
algorithms for symmetric matrix pencils (with P. Lancaster), in Operator Theory: Advances and
Applications, vol.40, The Gohberg
Anniversary Collection, Birkhauser, Basel, 1989,
- Variational principles and numerical algorithms for
symmetric matrix pencils, Ph.D. Thesis, University of Calgary, Calgary,
spectral problems for linear and quadratic matrix pencils, (with P.
- The unsolvability of inverse eigenvalue
problems for hermitian matrices almost
everywhere, Math. Numer. Sinica,
class of iterative algorithms for solving inverse eigenvalue
problems, Math. Numer. Sinica,
- The unsolvability of inverse algebraic eigenvalue
problems almost everywhere, (with J.G.
Comp. Math. 4 (1986):212-236