Department of Mathematics
University of Kentucky
Lexington, KY 40506-0027

Office:  735 Patterson Office Tower
Phone:  859-257-4653
Email:   qye3 “at” uky (dot) edu
FAX:     859-257-4078

Publications - Papers reviewed by Math. Review is listed in MathSciNet.

  1. Complex Unitary Recurrent Neural Networks using Scaled Cayley Transform, (with K.D. Maduranga and K. Helfrich), arXiv:1811.04142 [stat.ML], Proceedings of the Thirty-Third AAAI (Association for the Advancement of Artificial Intelligence) Conference on Artificial Intelligence ( AAAI-19)
  2. 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 80:1969-1978, 2018.
  3. State inference of RNA secondary structures with deep recurrent neural networks , (with D. Willmott and D. Murrugarra), ( Preprint.)
  4. Preconditioning for Accurate Solutions of Linear Systems and Eigenvalue Problems, Preprint available at arXiv:1705.04340 [math.NA].
  5. 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), 155–187.
  6. Accurate inverses for computing eigenvalues of extremely ill-conditioned matrices and differential operators, arXiv:1512.05292 [math.NA], Math. Comp. 87 (2018), 237-259
  7. Deflation by restriction for the inverse-free preconditioned Krylov subspace method , (with Q. Liang), Numerical Algebra, Control and Optimization, 6(2016): 55 - 71.
  8. Outlier Detection in the Framework of Dimensionality Reduction , (with W. Zhi), Int. J. Patt. Recogn. Artif. Intell. , 29 (2015):1550017 [19 pages].
  9. Discrete Hessian Eigenmap Algorithm for Dimensionality Reduction , (with W. Zhi), J. Comp. Applied Math., 278(2015):197–212.
  10. Computing Singular Values of Large Matrices With Inverse Free Preconditioned Krylov Subspace Method , (with Q. Liang), Electron. Trans. Numer. Anal.,, 42(2014):197-221.
  11. Relative perturbation theory for diagonally dominant matrices, (with M. Dailey and F. M. Dopico), SIAM J. Matrix Anal. Appl.,, 35(2014), 1303–1328.
  12. 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), 904–930.
  13. Simultaneous Similarity Reductions for a Pair of Matrices to Condensed Forms (with R.C. Li), Comm. Math. Statis., 2(2014):139-153.
  14. Computing Exponentials of Essentially Non-negative Matrices Entrywise to High Relative Accuracy (with J. Xue), Math. Comp.,, 82 (2013), 1577-1596.
  15. Analysis of Alignment Algorithms with Mixed Dimensions for Dimensionality Reduction, (with W. Zhi) Numer. Linear Algebra Appl., 20(2013):369-384.
  16. Error Bounds for the Lanczos Methods for Approximating Matrix Exponentials, SIAM J. Numer. Anal. 51(2013), 68–87
  17. Infinite matrices bounded on weighted L1 spaces, (with J. Williams) Linear Algebra Appl. 438 (2013), no. 12, 4689–4700.
  18. Eigenvalue Bounds for an Alignment Matrix in Manifold Learning (with W. Zhi), Linear Algebra and its Applications, 436(2012):2944–2962.
  19. Tikhonov regularization based on generalized Krylov subspace methods (with L. Reichel and F. Sgallari), Applied Numerical Mathematics 62 (2012) : 1215–1228
  20. Inexact Subspace Iterations For the Generalized Eigenvalue Problems (with P. Zhang), Linear Algebra and its Applications, 434 (2011):1697-1715.
  21. 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.
  22. A Block Inverse-free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems (with P. Quillen), J. Comp. Applied Math 233(2010):1298-1313
  23. Relative Perturbation Bounds for Eigenvalues of Diagonally Dominant Matrices, SIAM J. Matrix Anal. Appl. 31(2009):11-17.
  24. Simple square smoothing regularization operators (with L. Reichel) Electron. Trans. Numer. Anal. 33 (2008/09), 63–83.
  25. Entrywise Relative Perturbation Bounds for Exponentials of Essentially Nonnegative Matrices, (with J. Xue), Numer. Math. 110(2008):393--403.
  26. Computing 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.)
  27. A Generalized LSQR Algorithm, (with L. Reichel),  Numer. Linear Algebra Appl. 15(2008) : 643-660.
  28. Optimal Expansion of Subspaces for Eigenvector Approximations,  Linear Algebra Appl. 428(2008): 911-918.
  29. Analysis of an Algnment Algorithm for Nonlinear Dimensionality Reduction (with H. Zha, R.C. Li), BIT - Numerical Mathematics, 47, 2007: 873-885.
  30. Eigenvalues of An Alignment Matrix in Nonlinear Manifold Learning, (with C. Li, R.C. Li),   Comm.  Math. Sciences, 5(2007):313-329.
  31. 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.
  32. Krylov type subspace methods for matrix polynomials, (with L. Hoffnung and R.C. Li ), Linear Algebra Appl., 415 (2006):52–81.
  33. An Iterated Shift-and-invert Arnoldi Algorithm for  Quadratic Matrix Eigenvalue Problems, Applied Math. Comp. 172(2006):818-827.
  34. 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.
  35. Breakdown-free GMRES for Singular Systems, (with L. Reichel), SIAM J.  Matrix Anal. Appl., 26(2005):1001 – 1021.
  36. 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.
  37. An inverse free preconditioned  krylov subspace method for symmetric generalized eigenvalue problems (with G. Golub),  SIAM J. Sci. Comp.  24 (2002):312-334.
  38. Entrywise perturbation theory for diagonally dominant M-matrices with applications, (with A. Alfa, J. Xue), Numer. Math.  90 (2002):401-414.
  39. Accurate computation for the smallest eigenvalue of a diagonally dominant M-matrices, (with A. Alfa, J. Xue),   Math. Comp.  71 (2002):217-236.
  40. 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.
  41. 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.)
  42. Inexact Inverse Iterations for the Generalized Eigenvalue Problems, (with G. Golub), BIT - Numerical Mathematics,  40 (2000): 672-684.
  43. 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.
  44. 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.
  45. Entrywise perturbation theory for rate matrices of GI/M/1 type Markov chains, (with A. Alfa, J. Xue),  Stoch. Models 16 (2000):361-375.
  46. 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.
  47. Inexact preconditioned conjugate gradient method with inner-outer iteration, (with   G. Golub), SIAM J. Sci. Comp. 21 (2000):1305-1320.
  48. Analysis of finite precision bi-conjugate gradient algorithm for nonsymmetric linear systems, (with Charles Tong),  Math. Comp. 69 (2000):1559-1575.
  49. 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.
  50. 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.
  51. A variational principle for eigenvalues of pencils of Hermitian matrices, (with P. Binding, B. Najman), Integral Equations and Operator Theory,  35 (1999): 398-422.
  52. 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.
  53. 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.
  54. A Mixed Product Krylov Subspace method for Solving Nonsymmetric Linear Systems, (with T. F. Chan), Asian J. Math. 1 (1997):422-434.
  55. A linear system solver based on a modified Krylov subspace method for breakdown recovery, (with Charles Tong), Numer. Alg. 12 (1996):233-251.
  56. 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.
  57. 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.
  58. An adaptive block Lanczos algorithm, Numer. Alg. 12 (1996):97-110.
  59. On  close  eigenvalues  of  tridiagonal matrices, Numer. Math. 70 (1995):507-514.
  60. Variational principles for indefinite eigenvalue problems, (with P.A. Bining), Linear Algebra Appl. 218 (1995):251-262
  61. A breakdown-free variation of the nonsymmetric Lanczos algorithms, Math. Comp. 62 (1994):179-207.
  62. Low rank perturbations of strongly definitizable transformations and matrix polynomials,  (with P. Lancaster, A. Marcus), Linear Algebra and Appl. 198 (1994):3-29.
  63. Strongly definitizable linear pencils in Hilbert space,  (with P. Lancaster, A. Shkalikov), Integral Equations Operator Theory, 17 (1993):338-360.
  64. Rayleigh-Ritz and Lanczos methods for symmetric matrix pencils, (with P. Lancaster), Linear Algebra Appl. 185 (1993):173-201.
  65. Definitizable hermitian matrix pencils,  (with P. Lancaster),  Aequationes Mathematicae 46  (1993):44-55.
  66. A minimax characterization for eigenvalues of Hermitian pencils II (with B. Najman), Linear Algebra Appl. 191 (1993):183-197.
  67. Some general variational principles, (with P. A. Binding), Proc. Amer. Math. Soc. 114 (1992):107-114
  68. A convergence analysis of nonsymmetric Lanczos algorithms,  Math. Comp. 56 (1991):677-691.
  69. Variational principles without definiteness conditions,  (with P. Binding), SIAM J.  Math.  Anal.  22 (1991):1575-1583
  70. A minimax characterization for eigenvalues of hermitian pencils, (with B. Najman), Linear Alg. Appl. 144 (1991):217-230
  71. Variational and numerical methods for symmetric matrix pencils,  (with P. Lancaster), Bulletin of  Austr. Math. Soc. 43(1991):1-17
  72. 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.
  73. Variational principles and numerical algorithms for symmetric matrix pencils, Ph.D. Thesis, University of Calgary, Calgary, Canada, 1989.
  74.  Inverse spectral problems for linear and quadratic matrix pencils, (with P. Lancaster) Linear Alg.Appl. 107 (1988):293-309.
  75. The unsolvability of inverse eigenvalue problems for hermitian matrices almost everywhere, Math. Numer. Sinica, 9(1987):225-232.
  76. A class of iterative algorithms for solving inverse eigenvalue problems, Math. Numer. Sinica, 9(1987):144-153.
  77. The unsolvability of inverse algebraic eigenvalue problems almost everywhere, (with J.G. Sun), J. Comp.  Math.  4 (1986):212-236