research

RESEARCH PAGE of QIANG YE

My research interest includes numerical analysis/scientific computing, large matrix computations, operator theory, and various applied problems.

Here is a LIST of PUBLICATIONS. Below is a list by areas/problems.

Related software can be downloaded HERE.

This link gives those publications in Math. Review in AMS’s MathSciNet

Large Scale Matrix Eigenvalue Problems:

A Block Inverse-free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems (with P. Quillen), to appear in J. Comp. Applied Math.
Optimal Expansion of Subspaces for Eigenvector Approximations, Linear Algebra Appl. 428 (2008): 911-918.
Krylov type subspace methods for matrix polynomials, (with L. Hoffnung and R.C. Li ), Linear Algebra Appl., 415 (2006):52–81.
An Iterated Shift-and-invert Arnoldi Algorithm for Quadratic Matrix Eigenvalue Problems, Applied Math. Comp. 172 (2006):818-827.
Algorithm 845: EIGIFP: A MATLAB Program for Solving Large Symmetric Generalized Eigenvalue Problems, (with James Money), ACM Transaction on Mathematical Softwares, 31 (2005):270-279.
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.
An inverse free preconditioned krylov subspace method for symmetric generalized eigenvalue problems (with G. Golub), SIAM J. Sci. Comp. 24 (2002):312-334.
Inexact Inverse Iterations for the Generalized Eigenvalue Problems, (with G. Golub), BIT - Numerical Mathematics, 40 (2000): 672-684.
ABLE: an Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems, (with Z. Bai and D. Day), SIAM J. Matrix Anal. Appl. 20 (1999):1060-1082.
An adaptive block Lanczos algorithm, Numer. Alg. 12 (1996):97-110.
On close eigenvalues of tridiagonal matrices, Numer. Math. 70 (1995):507-514.
A breakdown-free variation of the nonsymmetric Lanczos algorithms, Math. Comp. 62 (1994):179-207.
Rayleigh-Ritz and Lanczos methods for symmetric matrix pencils, (with P. Lancaster), Linear Algebra Appl. 185 (1993):173-201.
A convergence analysis of nonsymmetric Lanczos algorithms, Math. Comp. 56 (1991):677-691.

High Relative Accuracy Algortihms and Applications in Stochastic Models:

Entrywise Relative Perturbation Bounds for Exponentials of Essentially Nonnegative Matrices, (with Jungong Xue), Numer. Math. 110(2008):393--403.

Computing Singular Values of Diagonally Dominant Matrices to High Relative Accuracy, Math. Comp. 77 (2008), 2195-2230.
Relative Perturbation Bounds for Eigenvalues of Diagonally Dominant Matrices, to appear in SIAM J. Matrix Anal. Appl.
Entrywise perturbation theory for diagonally dominant M-matrices with applications, (with A. Alfa, J. Xue), Numer. Math. 90 (2002):401-414.
Accurate computation for the smallest eigenvalue of a diagonally dominant M-matrices, (with A. Alfa, J. Xue), Math. Comp. 71 (2002):217-236.

Accurate 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.)

Perturbation 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.
High 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 (2000):361-375.

Iterative Methods for Large Linear Systems of Equations:

A Generalized LSQR Algorithm, (with L. Reichel), Numer. Linear Algebra Appl. 15 (2008) : 643-660.
Breakdown-free GMRES for Singular Systems, (with L. Reichel), SIAM J. Matrix Anal. Appl., 26 (2005):1001 – 1021.
Residual Replacement Strategies for Krylov Subspace Iterative Methods for the Convergence of True Residuals, (with H. van der Vorst), SIAM J. Sci. Comp. 22 (2000):836-852.
Inexact preconditioned conjugate gradient method with inner-outer iteration, (with G. Golub), SIAM J. Sci. Comp. 21 (2000):1305-1320.
Analysis of finite precision bi-conjugate gradient algorithm for nonsymmetric linear systems, (with Charles Tong), Math. Comp. 69 (2000):1559-1575.
A Mixed Product Krylov Subspace method for Solving Nonsymmetric Linear Systems, (with T. F. Chan), Asian J. Math. 1 (1997):422-434.
A linear system solver based on a modified Krylov subspace method for breakdown recovery, (with Charles Tong), Numer. Alg. 12 (1996):233-251.

Dimensionality Reduction in Data Analysis

Analysis of an Algnment Algorithm for Nonlinear Dimensionality Reduction (with H. Zha, R.C. Li), BIT - Numerical Mathematics, 47, 2007: 873-885.
Eigenvalues of An Alignment Matrix in Nonlinear Manifold Learning, (with C. Li, R.C. Li), Comm. Math. Sciences, 5(2007):313-329.

Model Reductions for Linear Circuits

Error 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 (1999):133-141.
Error Estimation of the Pade Approximation of Transfer Functions Via the Lanczos Process, (with Z. Bai), Electronic Transaction of Numerical Analysis, 7 (1998):1-17.
On 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.

Variational Principles for Matrix/Operators Pencils

A variational principle for eigenvalues of pencils of Hermitian matrices, (with P. Binding, B. Najman), Integral Equations and Operator Theory, 35 (1999): 398-422.
Variational principles for indefinite eigenvalue problems, (with P.A. Bining), Linear Algebra Appl. 218 (1995):251-262
A minimax characterization for eigenvalues of Hermitian pencils II (with B. Najman), Linear Algebra Appl. 191 (1993):183-197.
Some general variational principles, (with P. A. Binding), Proc. Amer. Math. Soc. 114 (1992):107-114
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, pp.247-278.
Variational principles and numerical algorithms for symmetric matrix pencils, Ph.D. Thesis, University of Calgary, Calgary, Canada, 1989.

Self-adjoint Matrix/Operator in an Indefinite Inner Product

Low rank perturbations of strongly definitizable transformations and matrix polynomials, (with P. Lancaster, A. Marcus), Linear Algebra and Appl. 198 (1994):3-29.
Strongly definitizable linear pencils in Hilbert space, (with P. Lancaster, A. Shkalikov), Integral Equations Operator Theory, 17 (1993):338-360.
Definitizable hermitian matrix pencils, (with P. Lancaster), Aequationes Mathematicae 46 (1993):44-55.

Inverse Eigenvalue Problems

Inverse spectral problems for linear and quadratic matrix pencils, (with P. Lancaster) Linear Alg.Appl. 107 (1988):293-309.
The unsolvability of inverse eigenvalue problems for hermitian matrices almost everywhere, Math. Numer. Sinica, 9(1987):225-232.
A class of iterative algorithms for solving inverse eigenvalue problems, Math. Numer. Sinica, 9(1987):144-153.
The unsolvability of inverse algebraic eigenvalue problems almost everywhere, (with J.G. Sun), J. Comp. Math. 4 (1986):212-236

Miscellaneous Topics

Improving the Uniqueness of Surface Wave Inversion Using Multiple-Mode Dispersion Data, (with Y. Supranata, M. Kalinski), ASCE International Journal of Geomechanics 7 (2007): 333-343.
An 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.
Bounds for the width of the instability intervals in the Mathieu equation, (with P.N. Shivakumar), Operator Theory: Advances and Applications vol.87, Birkhauser, Basel, 1996, pp. 348 - 357.