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, Issue 4, 2008, Pages 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:

 

  • 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.
  • 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), to appear in Numer. Linear Algebra Appl.
  • 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 Eq. Oper. 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. on 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 Eq. Oper. 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.