RESEARCH INTEREST

• Numerical Analysis and Dynamical Systems

PUBLICATIONS

• ``The upper semicontinuity of the least squares problems,'' Progress in System and Control Theory} V, Birkh\"{a}user, 458-467, 1990.
• ``An algorithm based on weighted logarithmic barrier functions for linear complementarity problems'' (with T.-Y. Li), Arab. J. Sci. Eng. 15(4B), 679-685, 1990.
• ``A polynomial-time predictor-corrector algorithm for a class of linear complementarity problems'' (with T.-Y. Li), SIAM J. Optmi. 1(1), 83-92, 1991.
• ``Markov finite approximation of Frobenius-Perron operator'' (with T.-Y. Li), Nonlinear Anal. TMA 17(8), 759-772, 1991.
• ``High order approximation of the Frobenius-Perron operator'' (with Q. Du and T.-Y. Li), Appl. Math. Comp. 53, 151-171, 1993.
• ``An continuation algorithm for linear complementarity problems using an extrapolation technique,'' Linear Algb. Appl. 186, 199-214, 1993.
• ``Perturbation analysis of the projection of a point onto an affine set,'' Linear Algb. Appl. 191, 199-212, 1993.
• ``Projection solutions of Frobenius-Perron operator equations'' (with T.-Y. Li), Inter. J. Math. Math. Sci. 16(3), 465-484, 1993.
• ``Entropy - an introduction'' (with T.-Y. Li), Nankai Series Pure Appl. Math. Th. Phys. 4, World Scientific, 26-53, 1993.
• ``A closed range theorem for the Frobenius-Perron operator and its application to the spectral analysis,'' J. Math. Anal. Appl. 184(1), 156-167, 1994.
• ``The spectral analysis of Frobenius-Perron operators'' (with Q. Du and T.-Y. Li), J. Math. Anal. Appl. 184(2), 285-301, 1994.
• ``On the perturbation of the least squares solutions in Hilbert spaces'' (with L.-J. Huang), Linear Algb. Appl. 212/213, 487-500, 1994.
• ``The projection method for computing multi-dimensional absolutely continuous invariant measures'' (with A.-H. Zhou), J. Stat. Phys. 77(3/4), 899-908, 1994.
• ``A new approach to the Frobenius-Perron operator'' (with W. E. Hornor), J. Math. Anal. Appl. 187(3), 1047-1058, 1994.
• ``A scaled gradient projection method for linear complementarity problems,'' Nonconvex Optmi. Appl. 1, Kluwer Academic, 58-67, 1994.
• ``Piecewise linear Markov approximations of Frobenius-Perron operators associated with multi-dimensional transformations'' (with A.-H. Zhou), Nonlinear Anal. TMA 25(4), 399-408, 1995.
• ``Finite element approximations of Frobenius-Perron operators - a solution to Ulam's conjecture for multi-dimensional transformations''(with A.-H. Zhou), Physica D 92, 61-68, 1996.
• ``Computing invariant measures for piecewise convex transformations,'' J. Stat. Phys. 83(3/4), 623-635, 1996.
• ``Some ergodic theorems for piecewise monotonic transformations,'' J. Math. Anal. Appl. 202, 194-205, 1996.
• ``Perturbation of generalized inverses of linear operators in Hilbert spaces''(with L.-J. Huang), J. Math. Anal. Appl. 198, 506-515, 1996.
• ``Optimal perturbation results for least squares problems,'' Lecture Notes Oper. Res. 2, World Publishing, 47-55, 1996.
• ``Decomposition theorems for Koopman operators,'' Nonlinear Anal. TMA 28(6), 1011-1018, 1997.
• ``Absolutely continuous invariant measure of a piecewise concave mapping of [0,1],'' Nonlinear Anal. TMA 28(7), 1133-1140, 1997.
• ``Computing fixed densities of Markov operators defined by a stochastic kernel,'' Appl. Math. Lett. 10(3), 85-88, 1997.
• ``On the continuity of generalized inverses of linear operators in Hilbert spaces'' (with L.-J. Huang), Linear Algb. Appl. 262, 229-242, 1997.
• ``The point spectrum of Frobenius-Perron and Koopman operators,'' Proc. Amer. Math. Soc. 126(5), 1355-1361, 1998.
• ``A convergence rate analysis for Markov finite approximations to a class of Frobenius-Perron operators'' (with T.-Y. Li), Nonlinear Anal. TMA 31(5/6), 765-777, 1998.
• ``Computing fixed densities of a class of Frobenius-Perron operators'' (with A.-H. Zhou), Nonlinear Anal. TMA 32(3), 409-416, 1998.
• ``A maximum entropy method for solving Frobenius-Perron operator equations,'' Appl. Math. Comp. 93, 155-168, 1998.
• ``Perturbation results for projecting a point onto a linear manifold,'' SIAM J. Matrix Anal. Appl. 19(3), 696-700, 1998.
• ``New perturbation results for equality constrained least squares problems'' (with W.-H. Huang), Linear Algb. Appl. 272, 181-192,
• ``The invariant measure and its computation'' (with A.-H. Zhou), Adv. in Math. (in Chinese) 27(4), 309-323, 1998.
• ``On the perturbation of least squares problems with equality constraints,'' Linear and Multilinear Algb. 45, 35-47, 1998.
• ``The projection method for a class of Frobenius-Perron operators'' (with A.-H. Zhou), Appl. Math. Lett. 12, 71-74, 1999.
• ``Perturbation bounds for least squares problems with equality constraints,'' J. Math. Anal. Appl. 229, 631-638, 1999.
• ``A finite element method for the Frobenius-Perron operator equation'' (with A.-H. Zhou), Appl. Math. Comp. 102(2/3), 155-164, 1999.
• ``A generalization of a classic theorem in the perturbation theory for linear operators'' (with L.-J. Huang), J. Math. Anal. Appl. 239(1), 118-123, 1999.
• ``Computing fixed points of quasi-compact Frobenius-Perron operators'' (with A.-H. Zhou), Nonlinear Anal. TMA 39(2), 231-239, 2000.
• ``Absolutely continuous invariant measures for piecewise $C^2$ and expanding mappings in higher dimensions'' (with A.-H. Zhou), Disc. Cont. Dynam. Sys. 6(2), 451-458, 2000.
• ``Perturbation of systems of linear algebraic equations,'' Linear \& Multilinear Algb. 47, 119-127, 2000.
• ``Error estimates for quasi-compact Markov operators'' (with F. Y. Hunt), Nonlinear Anal. TMA 42(1), 85-95, 2000.
• ``On the spectrum of Frobenius-Perron operators'' (with A.-H. Zhou), J. Math. Anal. Appl. 250, 610-620, 2000.
• ``Lower and upper bounds in the perturbation of general linear algebraic equations,'' Applied Math. Letters 14, 49-52, 2001.
• ``On estimating absolutely continuous invariant measures'' (with A.-H. Zhou), Nonlinear Anal. TMA 43(6), 683-691, 2001.
• ``Representations for Moore-Penrose inverses in Hilbert spaces'' (with Y. Wei), Applied Math. Letters 14, 599-604, 2001.
• ``On the spectrum and pseudoinverse of a special bordered matrix'' (with W. Pye), Linear Alg. Appl. 331, 11-20, 2001.
• ``Relative errors versus residuals of approximate solutions to linear algebraic equations and least squares problems,'' Missouri J. Math. Sci. 13(1), 47-52, 2001.
• ``Parallel computation of invariant measures'' (with Z. Wang), Annals of Operations Research 103, 283-290, 2001.
• ``Constructive approximations of Markov operators on $L^1([0,1]^N)$'' (with A. Zhou), J. Stat. Phys. 105(5/6), 863-878, 2001.
• ``Approximation order analysis for the piecewise linear Markov method'' (with Z. Wang), Stochastic Anal. Appl. 19(6), 911-923, 2001.
• ``Minimal distance upper bounds for the perturbation of least squares problems in Hilbert spaces,'' Applied Math. Letters 15, 361-365, 2002.
• ``Another proof of the change of variable formula for $d$-dimensional integrals,'' Missouri J. Math. Sci. 14(1), 38-39, 2002.
• ``Structure preserving finite element approximations of Markov operators'' (with A. Zhou), Nonlinearity 15, 923-936, 2002.
• ``Maximum entropy approximation for Lyapunov exponents of chaotic maps" (with L. Mead), J. Math. Phys. 43(5), 2518-2522, 2002.
• ``Stochastic analysis of electrical circuits'' (with M. van Wyk), Chaos in Circuits and Systems}, Nonlinear Science Series B, Vol. 11, World Sci., G. Chen et al. ed., 215-236, 2002.
• ``Relative errors versus residuals of approximate solutions of weighted least squares problems in Hilbert space'' (with Y. Wei), Computers \& Math. with Appl. 44, 407-411, 2002.
• ``On the existence of solutions to equality constrained least squares problems in infinite dimensional Hilbert spaces,'' Applied Math. Compt. 131(2/3), 573-581, 2002.
• ``Bounds for perturbed solutions of linear operator equations in Hilbert space'' (with Y. Wei), Applied Math. Compt. 132(2/3), 293-298, 2002.
• ``Finite approximations of Markov operators'' (with T. Y. Li and A. Zhou), J. Compt. \& Applied Math. 147, 137-152, 2002.
• ``On the perturbation of the reduced minimum modulus of bounded linear operators," Applied Math. Compt. 140, 69-75, 2003.
• ``On the expression of generalized inverses of perturbed bounded linear operators,'' Missouri J. Math. Sci. 15(1), 40-47, 2003.
• ``New perturbation results on pseudo-inverses of linear operators in Banach spaces," Linear Alg. Appl. 362, 229-235, 2003.
• ``Markov chains and dynamic geometry of polygons" (with R. Hitt and X.-M. Zhang), Linear Alg. Appl. 367, 255-270, 2003.
• ``A Monte Carlo approach to piecewise linear Markov approximations of Markov operators'' (with D. Mao and A. Zhou), Monte Carlo Methods Appl. 9(4), 295-306, 2003.
• ``Lower and upper bounds for the perturbation of linear operator equations,'' Applied Math. Letters 17(1), 55-58, 2004.
• ``Approximations of Frobenius-Perron operators via interpolation'' (with N. Rhee), Nonlinear Anal. TMA 57(5/6), 831-842, 2004.
• ``The Perron-Frobenius theorem and limits in geometry'' (with T. Fay), Amer. Math. Monthly. 112(2), 171-175, 2005.
• ``A modified piecewise linear Markov approximation of Markov operators'' (with N. Rhee), Applied Math Comput. 174(1), 236-251, 2006.
• ``Some results on structured M-matrices with an application to wireless communications'' (with W. Pye and L. Zhao), Linear Alg. Appl. 416, 608-614, 2006.
• ``Power distribution/allocation in multirate wideband CDMA systems'' (with L. Zhao and J. Mark), IEEE Trans. Wireless Comm. 5(9), 2458-2467, 2006.
• ``The eigenvalue problem of a specially updated matrix'' (with G. Yao), Applied Math. Comput. 185(1), 415-420, 2007.
• ``Integral and nonnegativity perserving approximations of functions'' (with L. Eifler and N. Rhee), J. Math. Anal. Appl. 325(2), 889-897, 2007.
• ``The Maximum entropy method applied to stationary density computation'' (with L. Mead), Applied Math. Comput. 185(1), 658-666, 2007.
• ``Least squares approximations to lognormal sum distributions'' (with L. Zhao), IEEE Transac. Veh. Tech. 56(2), 991-997, 2007.
• ``A posteriori error estimates for Markov approximations of Frobenius-Perron operators'' (with C. Jin and A. Zhou), Nonlinear Anal. TMA} 67(3), 763-772, 2007.
• ``Web graphics for the computation of invariant measures'' (with Z. Wang and H. Yang), Applied Math. Comput. 187(2), 1442-1552, 2007.
• ``Eigenvalues of rank-one updated matrices with some applications'' (with A. Zhou), Applied Math. Letters 20, 1223-1226, 2007.
• ``Particular solutions of some elliptic partial differential equations via recursive formulas'' (with C. S. Chen), J. Univ. Sci. Tech. China 37(11), 1338-1347, 2007.
• ``Characteristic polynomials of some perturbed matrices'' (with A. Zhou), Applied Math. Comput. 199, 631-636, 2008.
• ``A spectrum theorem for perturbed linear operators'' (with A. Zhou), Applied Math. Comput. 201 (2008), 723-728.