Yuesheng Xu
Professor of Mathematics
E-mail: yxu@math.wvu.edu
Voice: +1 304 293 2011 ext. 2352(W)
Fax: +1 304 293 3982

Publications

Books and Specail Issues

2000

1999

1998-1997

1996

1995

1994

1993-1989

Selected Publications 

  1. Fast Collocation Methods for Second Kind Integral Equations (with Z. Chen and C. A. Micchelli), SIAM J. Numer. Anal., 40 (2002), 344-375. (pdf file)
  2. A Multilevel Method for Solving Operator Equations, (with Z. Chen and C. A. Micchelli), J. Math. Anal. Appl. to appear.
  3. A Factorization Method for Identification of Volterra Systems (with M. Brenner), J. Computational and Applied Math., to appear.
  4. Deterministic Convergence of an Online Stochastic Gradient Method for Neural Networks (with Wei Wu), J. Computational and Applied Math., to appear.
  5. Discrete Wavelet Petrov-Galerkin Methods (with Z. Chen and C. A. Micchelli), Advances in Computational Mathematics, 16 (2002), 1-28. (pdf file)
  6. Subdivision Schemes for Iterated Function Systems (withi C. A. Micchelli and T. Suaer), Proc. Amer. Math. Soc. 129 (2001), 1861-1872.
  7. Asymptotic Error Analysis of a Quadrature Method for Integral Equations with Green's Function Kernels (with William F. Ford, J. A. Pennline and Y. Zhao), J. Integral Equations Appl. 12 (2000), 349-384.
  8. Nonlinear Functionals of Wavelet Expansions - Adaptive Reconstruction and Fast Evaluation (with W. Dahmen and R. Schneider), Numer. Math. 86 (2000), 49-101.
  9. Hermite Interpolating Wavelets (with Z. Chen and C. A. Micchelli), in Lecture Notes in Scientific Computation, Edited by LuoluoLi, Zhongying Chen and Yongdong Zhang, International Culture Publishing Inc. (2000), 31-39, Beijing. (ISBN 7-5026-1176-2)
  10. A Construction of Interpolating Wavelets on Invariant Sets, (with Z. Chen and C. A. Micchelli), Math. Comp. 68 (1999), 1569-1587.
  11. Numerical Computation of a Heavily Loaded Flexible-beam Model, (with G. Chen and Z. Chen), Comm. Numer. Methods Engineering 15 (1999), 249-261.
  12. The Discrete Petrov-Galerkin Method for Second Kind Integral Equations, (with Z. Chen and J. Zhao), J. Integral Equations Appl. 11 (1999), 1-35.
  13. A construction of refinable sets for interpolating wavelets (with C. A. Micchelli and T. Sauer), Results in Mathematics 34 (1998), 359-372.
  14. The Petrov-Galerkin and Iterated Petrov-Galerkin Methods for Second Kind Integral Equations, (with Z. Chen), SIAM J. Numer. Anal. 35 (1998), 406-434.
  15. Wavelet Galerkin Methods for Systems of Multivariate IntegralEquations, (with C. A. Micchelli and Y. Zhao), J. Comp. Appl. Math. 86 (1997), 251-270.
  16. Geometric Distance between Oriented Curves, (with P. Bogacki and S. E. Weinstein), Advances in Computational Math. 7 (1997), 593-621.
  17. The Petrov-Galerkin Methods for Second Kind Integral Equations II: Multiwavelet Scheme, (with Z. Chen and C. A. Micchelli), Advances in Computational Mathematics 7 (1997), 199-233.
  18. Reconstruction and Decomposition Algorithms for BiorthogonalWavelets, (with Charles A. Micchelli), Multidimensional Systems and Signal Processing 8 (1997), 31-69
  19. Derivative Correction for Quadrature Formulas, (with W. F. Ford and Y. Zhao), Advances in Computational Mathematics 6 (1996), 139-157.
  20. Superconvergence of the Iterated Galerkin Methods for Hammerstein Equations, (with Hideaki Kaneko), SIAM J. Numer. Anal. 33 (1996), 1048-1064.
  21. Quadratures for Boundary Integral Equations of the First Kind with Logarithmic Kernels, (with Y. Zhao), J. Integral Equations Appl. 8 (1996), 239-268.
  22. A Extrapolation Method for a Class of Boundary Integral Equations, (with Y. Zhao), Math. Comp. 65 (1996), 587-610.
  23. Constrained Best Approximation in Hilbert Space III: Applications to n-Convex Functions, (with Frank Deutsch, Vasant Ubhaya andJoseph D. Ward), Constructive Approximation 12 (1996), 361-384.
  24. Degenerate Kernel Schemes by Wavelets for Nonlinear Integral Equations on the Real Line, (with Zuowei Shen), Applicable Analysis 59 (1995), 163-184.
  25. Dual Cones, Constrained n-Convex Lp-Approximation and Perfect Splines, (with Frank Deutsch and Vasant A. Ubhaya), J. Approx. Theory 80 (1995), 180-203.
  26. Constrained Lp-Approximation by Generalized n-ConvexFunctions Induced by ECT-Systems, (with V. A. Ubhaya), J. Approx. Theory 80 (1995), 423-449.
  27. Degree Reduction of Bezier Curves by Uniform Approximation with Endpoint Interpolation, (with P. Bogacki and S. E. Weinstein), Computer-Aided Design 27 (1995), 651-661.
  28. Using the Matrix Refinement Equation for the Construction of Wavelets II: Smooth Wavelets on [0,1], (with Charles A. Micchelli), in Approximation and Computation, A Festschrift in Honor of Walter Gautschi, R. Zahar (ed.), Birkhauser, Boston, 1995, 435-457.
  29. Weakly Singular Fredholm Integral Equations I: Singularity Preserving Wavelet Galerkin Methods, in Approximation Theory VIII, Vol. 2: Wavelet and Multilevel Approximation, C. K. Chui and L. L. Schumaker (eds.), World Scientific, Singapore, 1995, 283-300.
  30. Weakly Singular Fredholm Integral Equations II: Singularity Preserving Wavelet Collocation Methods, in Approximation Theory VIII, Vol. 2: Wavelet and Multilevel Approximation, C. K. Chui and L. L. Schumaker (eds.), World Scientific, Singapore, 1995, 167-178.
  31. Recursions for Tchebycheff B-Splines and Their Jumps, in Approximation, Wavelets and Applications, S. P. Singh (ed.), NATO ASI Series, Vol. 454, Kluwer, 1995, 543-555.
  32. Quadratures for Improper Integrals and their Applications in Integral Equations, (with Yunhe Zhao), {\it Proceedings of Symposia in Applied Mathematics}, 48 (1994), 409-413.
  33. Using the Matrix Refinement Equation for the Construction of Wavelets on Invariant Sets, (with Charles A. Micchelli), Appl. Comp. Harmonic Anal., 1 (1994), 391-401.
  34. Singularity Preserving Galerkin Methods for Weakly Singular Fredholm Integral Equations, (with Yanzhao Cao), J. Integral Equations Appl. 6 (1994), 303-334.
  35. Gaussian-Type Quadratures for Weakly Singular Integrals and their Applications to the Fredholm Integral Equation of the Second Kind, (with Hideaki Kaneko), Math. Comp. 62 (1994), 739-753.
  36. Extrapolation Methods for Nonlinear Boundary Integral Equations, (with William F. Ford and Yunhe Zhao), in Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics, W. F. Ames (ed.), (1994), 1249-1252.
  37. Singularity Preserving Collocation Method for Weakly Singular Fredholm Integral Equations of the Second Kind, (with R. Hu and H. Kaneko), in Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics, W. F. Ames (ed.), (1994), 1311-1314.
  38. Numerical Solutions for Weakly Singular Hammerstein Equations and their Superconvergence, (with H. Kaneko and R. Noren), J. Integral Equations Appl. 4 (1992), 391-407.
  39. Degree Reduction of Bezier Curves by Approximation and Interpolation, (with S. E. Weinstein), The Proceedings of 6th South Eastern Approximation Theorists International Conference, George A. Anastassiou (ed.), pp. 503-512, Marcel Dekker, 1992.
  40. Degenerate Kernel Method for Multi-variable Hammerstein Equations, (with H. Kaneko and G. Kerr), Appl. Numer. Math. 10 (1992), 473-479.
  41. Numerical Solutions for Weakly Singular Fredholm Integral Equations of the Second Kind, (with H. Kaneko), Appl. Numer. Math. 7 (1991), 167-177.
  42. Best Lp Approximation by Multiple Constraints for 1£ p<¥ (with J. J. Swetits and S. E. Weinstein), J. Approx. Theory 65 (1991), 90-108.
  43. A Duality Approach to Best Uniform Convex Approximation, (with S. E. Weinstein), J. Math. Anal. Appl. 160 (1991), 314-322.
  44. Degenerate Kernel Method for Hammerstein Equations, (with H. Kaneko), Math. Comp. 65 (1991), 141-148.
  45. On the Characterization and Computation of Best Monotone Approximation in Lp[0,1] for 1 £ p<¥, (with J. J. Swetits, and S. E. Weinstein), J. Approx. Theory 60 (1990), 58-69.
  46. Best Quasi-Convex Uniform Approximation, (with S. Weinstein), J. Math. Anal. Appl. 152 (1990), 240-251.
  47. Regularity of the Solution of Hammerstein Equations with Weakly Singular Kernel, (with H. Kaneko and R. Noren), Integral Equation and Operator Theory 13 (1990), 660-670.
  48. Approximation in Lp[0,1] by n-Convex Functions, (with J. J. Swetits and S. Weinstein), Numer. Funct. Anal. Optimiz. 11 (1990), 167-179.
  49. Best Piecewise Monotone Uniform Approximation, (with V.A. Ubhaya and S. E. Weinstein), J. Approx. Theory 63 (1990), 375-383.
  50. A Characterization of the Solution of A Fredholm Integral Equation with L¥ Forcing Term, (with H. Kaneko and R. Noren), J. Integral Equations Appl. 2 (1990), 581-594.
  51. The Computation of A Best Monotone Lp Approximation for 1£ p<¥, (with J. J. Swetits and S. E. Weinstein), Numer. Funct. Anal. Optimiz. 11 (1990), 811-822.
  52. The Characterization of Best n-Convex Approximation in Lp[0,1] for 1 £ p<¥, (with J. J. Swetits and S. E. Weinstein), in Approximation Theory VI, C. K. Chui, L. L. Schumaker and J. D. Ward (eds.), pp. 651-654, Academic Press, 1989.
  53. Uniform Approximation by Piecewise Monotone Functions with Free Knots, (with S. E. Weinstein), in Approximation Theory VI, C. K. Chui, L. L. Schumaker and J. D. Ward (eds.), pp. 671-674, Academic Press, 1989. 

Books and Specail Issues

Publications

Books and Specail Issues

2000

1999

1998-1997

1996

1995

1994

1993-1989

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Email: yxu@math.wvu.edu     Last Modified: 10/14/2001