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Yuesheng Xu

Yuesheng Xu


Professor
Department of Mathematics & Statistics

Contact Information


2300 ENGR & COMP SCI BLDG
NORFOLK, VA 23529

Email: y1xu@odu.edu

Phone: 757-683-4969

Education/Credentials



  • Articles

    Li, Z., Song, G. H., and Xu, Y. (2018). A fixed-point proximity approach to solving the support vector regression with the group lasso regularization. International Journal of Numerical Analysis and Modeling, 15 (1-2), pp. 154-169.
    Cao, Y., Jiang, Y., and Xu, Y. (2017). A fast discrete spectral method for stochastic partial differential equations. Advances in Computational Mathematics, 43, pp. 973-998.
    Benner, S., Sung, L., Wang, Z., and Xu, Y. (2017). A Finite element method for the one-dimentional prescribed curvature problem. International Journal of Numerical Analysis and Modeling, 14, pp. 646-669.
    Chen, Z., Zhang, J., and Xu, Y. (2017). A second - order hybrid finite volume method for solving the Stokes equation. Applied Numerical Mathematics, 119, pp. 213-224.
    Wang, R., and Xu, Y. (2017). Functional reproducing kernel Hilbert spaces for non-point-evaluation functional data. Applied and Computational Harmonic Analysis
    Long, W., Lu, Y., Shen, L., and Xu, Y. (2017). High-resolution image reconstruction: An env l1/TV model and a xed-point proximity. International Journal of Numerical Analysis and Modeling,, 14, pp. 255-282.
    Lu, J., Shen, L., Xu, C., and Xu, Y. (2017). Multiplicative noise removal with sparisty-aware optimization model. Inverse Problems and Imaging, 11, pp. 949-974.
    Li, Q., Xu, Y., and Zhang, N. (2017). Two-step fixed point prximity algorithms for multi-block separable convex problems. Journal of Scientific Computing, 70, pp. 1204-1228.
    Feiglin, D., Krol, A., Li, S., Schmidtlein, C. R., Zhang, J., and Xu, Y. (2017). Preconditioned alternating projection algorithm for solving the penalized-likelihodd SPECT reconstruction problem. Physica Medica, 38, pp. 23-35.
    Liu, Y., Shen, L., Xu, Y., and Yang, H. (2016). A collocation method solving integral equation models for image restoration. Journal of Integral Equations and Applications, 28 (2), pp. 263-307.
    Krol, A., Li, S., Wu, Z., Zeng, X., and Xu, Y. (2016). Reducing staircasing artifacts in SPECT reconstruction by an inmal convolution regularization. Journal of Computational Mathematics, 34, pp. 626-647.
    Chen, Z., and Zhang, Y. (2015). A construction of higher-order nite volume methods. Mathematics of Computation, 84, pp. 599-628.
    Ma, Y., and Xu, Y. (2015). Computing oscillatory integrals: Partition of the integration interval based on the singularity and the wave number of the integrand. Science in China Mathematics, 45 (8), pp. 1133-1152.
    Chen, F., Shen, L., Suter, B., and Xu, Y. (2015). A fast and accurate algorithm for l1 minimization problems in compressive sampling. EURASIP Journal on Advances in Signal Processing, 1 (1),
    Jiang, Y., Wang, B., and Xu, Y. (2014). A fast Fourier-Galerkin method solving a boundary integral equation for the biharmonic equation. SIAM Journal on Numerical Analysis, 52, pp. 2530-2554.
    Jiang, Y., and Xu, Y. (2014). Fast computation of the multidimensional discrete Fourier transform and discretebackward Fourier transform on sparse grids. Mathematics of Computation, 83, pp. 2347-2384.
    Chen, Z., Xu, Y., and Zhang, Y. (2014). Higher-order finite volume methods II: Inf-sup condition and uniform local ellipticity. Journal of Computational and Applied Mathematics, 265, pp. 96-109.
    Chen, F., Shen, L., Xu, Y., and Zeng, X. (2014). The Moreau envelope approach for the L1/Tv image denoising model. Inverse Problems and Imaging, 8 (53),
    Xu, Y., and Zheng, T. (2011). Optimal H2 model reduction for large scale MIMO systems via tangential interpolation. Int. J. Numer. Anal. Model., 8, pp. 174-188.
    Micchelli, C. A., Shen, L., and Xu, Y. (2011). Proximity algorithms for image models: Denosing. Inverse Problems, 27 (4), pp. 30 pp.
    Song, G., and Xu, Y. (2010). Approximation of high dimensional kernel matrices by multilevel circulant matrices. J. Complexity, 26 (4), pp. 375-405.
    Song, G., and Xu, Y. (2010). Approximation of kernel matrices by circulant matrices and its application in kernel selection methods. Front. Math. China, 5, pp. 123-160.
    Wang, B., Wang, R., and Xu, Y. (2010). Fast Fourier-Galerkin methods for first-kind logarithmic-kernel integral equations on open arcs. Science in China, 53, pp. 1-22.
    Jiang, Y., and Xu, Y. (2010). Fast Fourier-Galerkin methods for solving singular boundary integral equations: Numerical integration and precondition. J. Comput. Appl. Math. (234),
    Qian, T., Wang, R., Xu, Y., and Zhang, H. (2010). Orthonormal bases with nonlinear phases. Advances in Computational Mathematics, 33, pp. 75-95.
    Lu, Y., Shen, L., and Xu, Y. (2010). Integral equation models for image restoration: High accuracy methods and fast algorithms. Inverse Problems, 26 (4), pp. 32pp.
    Jiang, Y., and Xu, Y. (2010). Fast discrete algorithms for sparse Fourier expansions of high dimensional functions. J. Complexity, 26 (1), pp. 51-81.
    Cao, Y., Wu, B., and Xu, Y. (2009). A fast collocation method for solving stochastic integral equations. SIAM Journal on Numerical Analysis, 47, pp. 3744-3767.
    Chen, Z., Wu, B., and Xu, Y. (2009). Fast multilevel augmentation methods for solving Hammerstein equations. SIAM Journal on Numerical Analysis, 47, pp. 2321-2346.
    Wang, R., Xu, Y., and Zhang, H. (2009). Fast nonlinear Fourier expansions. Advances in Adaptive Data Analysis, 1, pp. 373-405.
    Qian, T., Xu, Y., Yan, D., Yan, L., and Yu, B. (2009). Fourier spectrum characterization of Hardy spaces and applications. Proc. Amer. Math. Soc., 137,
    Brenner, M., Jiang, Y., and Xu, Y. (2009). Multiparameter regularization for Volterra kernel identification via multiscale collocation methods. Adv. Comput. Math., 31, pp. 421-455.
    Micchelli, C., Zhang, H., and Xu, Y. (2009). Optimal learning of bandlimited functions from localized sampling. Journal of Complexity, 25 (2), pp. 85-114.
    Xu, Y., and Zhang, H. (2009). Recent mathematical development on empirical mode decomposition. Advances in Adaptive Data Analysis, 1, pp. 681-702.
    Xu, Y., and Zhang, H. (2009). Refinement of reproducing kernels. Journal of Machine Learning Research, 10 (Jan), pp. 107-140.
    Zhang, H., Xu, Y., and Zhang, J. (2009). Reproducing kernel Banach spaces in machine learning. J. Machine Learning Research, 10, pp. 2741-2775.
    Chen, Z., Nelakanti, G., Xu, Y., and Zhang, Y. (2009). A fast collocation method for eigen-problems of weakly singular integral operators. J. Scientific Computing, 41, pp. 256-272.
    Cai, H., and Xu, Y. (2008). A fast Fourier-Galerkin method for solving singular boundary integral equations. SIAM Journal on Numerical Analysis, 46, pp. 1965-1984.
    Chen, Z., Wu, B., and Xu, Y. (2008). Fast collocation methods for high dimensional weakly singular integral equations. J. Integral Equations Appl., 20,
    Chen, Z., Xu, Y., and Yang, H. (2008). Fast collocation methods for solving ill-posed integral equations of the rst kind. Inverse Problems, 24,
    Chen, Z., Lu, Y., Xu, Y., and Yang, H. (2008). Multi-parameter Tikhonov regularization for linear ill-posed operator equations. J. Comput. Math., 26, pp. 37-55.
    Micchelli, C. A., Xu, Y., and Zhang, H. (2008). On translation invariant operators which preserve the B-spline recurrence., 28 (2), pp. 157-169.
    Chen, Z., Wu, B., and Xu, Y. (2007). Fast numerical collocation solutions of integral equations. Commun. Pure Appl. Anal., 6, pp. 643-666.
    Cao, Y., Huang, M., Liu, L., and Xu, Y. (2007). Hybrid collocation methods for Fredholm integral equatioins with weakly singular kernels. Appl. Numer. Math., 57, pp. 549-561.
    Lu, Y., Shen, L., and Xu, Y. (2007). Multi-parameter regularization methods for high-resolution image reconstruction with displacement errors. IEEE Trans. Circuits Systems, 54, pp. 1788-1799.
    Chen, Q., Micchelli, C., and Xu, Y. (2007). On the matrix completion problem for multivariate lter bank construction. Advances in Computational Mathematics, 26, pp. 173-204.
    Xu, Y., and Zhang, H. (2007). Refinable kernels. J. Mach. Learn. Res., 8, pp. 2083-2120.
    Chen, Z., Xu, Y., and Yang, H. (2006). A multilevel augmentation method for solving ill-posed operator equations. Inverse Problems, 22, pp. 155-174.
    Schneider, R., Xu, Y., and Zhou, A. (2006). An analysis of discontinuous Galerkin methods for elliptic problems. Advances in Computational Mathematics, 25, pp. 259-286.
    Liu, S., and Xu, Y. (2006). Galerkin methods based on Hermite splines for singular perturbation problems. SIAM Journal on Numerical Analysis, 43, pp. 2607-2623.
    Liu, B., Riemenschneider, S., and Xu, Y. (2006). Gearbox fault diagnosis using empirical mode decomposition and Hilbert spectrum. Mechanical Systems and Signal Processing, 20, pp. 718-734.
    Chen, Z., Wu, B., and Xu, Y. (2006). Multilevel augmentation methods for dierential equations. Advances in Computational Mathematics, 24, pp. 213-238.
    Huang, M., and Xu, Y. (2006). Superconvergence of the iterated hybrid collocation method for weakly singular Volterra integral equations. J. Integral Equations, 18, pp. 83-116.
    Xu, Y., and Yan, D. (2006). The Bedrosian identity for the Hilbert transform of product functions. Proc. Amer. Math. Soc., 134, pp. 2719-2728.
    Xu, Y., Liu, B., Liu, J., and Riemenschneider, S. (2006). Two-dimensional empirical mode decomposition by nite elements. Proc. R. Soc., A- 462, pp. 3081-3096.
    Micchelli, C., Xu, Y., and Zhang, H. (2006). Universal kernels. J. Machine Learning Research, 7, pp. 2651-2667.
    Chen, Q., Huang, N., Riemenschneider, S., and Xu, Y. (2006). A B-spline approach for empirical mode decompositions. Advances in Computational Mathematics, 24 (1-4), pp. 171-195.
    Wang, Y., and Xu, Y. (2005). A fast wavelet collocation method for integral equations on polygons. J. Integral Equations Appl., 17, pp. 277-330.
    Wu, W., Feng, G., Li, Z., and Xu, Y. (2005). Deterministic convergence of an online gradient method for BP neural networks. IEEE Transaction on Neural Networks, 16, pp. 533-540.
    Chen, Z., Wu, B., and Xu, Y. (2005). Error control strategies for numerical integrations in fast collocation methods. Northeastern Mathematics Journal, 21, pp. 233-252.
    Chen, Z., Wu, B., and Xu, Y. (2005). Multilevel augmentation methods for operator equations. Numerical Mathematics, A Journal of Chinese Universities (English Series), 14, pp. 31-55.
    Liu, Y., and Xu, Y. (2005). Piecewise linear spectral sequences. Proc. Amer. Math. Soc., 133, pp. 2297-2308.
    Lu, Y., Shen, L., and Xu, Y. (2005). Shadow block iteration for solving linear systems obtained from wavelet transforms. Appl. Comp. Harmonic Anal., 19, pp. 359-385.
    Xu, Y., and Zou, Q. (2005). Tree wavelet approximations with applications. Sciences in China Ser. A Math, 48, pp. 680-702.
    Chen, Q., Micchelli, C. A., and Xu, Y. (2005). Biorthogonal multivariate filter banks from centrally symmetric matrices. Linear Algebra and its Applications, 402, pp. 111-125.
    Xu, Y., and Zhou, A. (2004). Fast Boolean approximation methods for solving integral equations in High dimensions. J. Integral Equations Appl., 16, pp. 83-110.
    Xu, Y., Chen, H., and Zou, Q. (2004). Limit values of derivatives of the Cauchy integrals and computation of the logarithmic potential. Computing, 73, pp. 237-295.
    Chen, Q., and Xu, Y. (2004). The Cascade algorithms for the numerical computation of refinable functions. Advances in Computational Mathematics, 20, pp. 17-24.
    Fang, W., Wang, Y., and Xu, Y. (2004). An implementation of fast wavelet Galerkin methods for integral equations of the second kind. Journal of Scientific Computing, 20 (2), pp. 277-302.
    Cao, Y., Herdman, T., and Xu, Y. (2003). A hybrid collocation method for Volterra integral equations with weakly singular kernels. SIAM Journal on Numerical Analysis, 41, pp. 264-281.
    Xu, Y., and Zhou, Q. (2003). AdaptiveWavelet Methods for Elliptic Operator Equations with Nonlinear Terms. Advances in Computational Mathematics, 19, pp. 99-146.
    Chen, Q., Micchelli, C., Peng, S., and Xu, Y. (2003). Multivariate lter banks having a matrix factorization. SIAM Journal on Matrix Analysis and Its Applications, 25, pp. 517-531.
    Wu, W., and Xu, Y. (2002). Deterministic convergence of an online gradient method for neural networks. Journal of Computational and Applied Mathematics, 144, pp. 335-347.
    Chen, Z., Micchelli, C., and Xu, Y. (2002). Fast collocation methods for second kind integral equations. SIAM Journal on Numerical Analysis, 40, pp. 344-375.
    Brenner, M., and Xu, Y. (2002). A factorization method for identification of Volterra systems. Journal of Computational and Applied Mathematics,, 144 (1-2), pp. 105-117.
    Chen, Z., Micchelli, C. A., and Xu, Y. (2002). Discrete wavelet Petrov-Galerkin methods. Advances in Computational Mathematics, 16 (1), pp. 1-28.
    Fang, W., Ma, F., and Xu, Y. (2002). Multilevel iteration methods for solving integral equations of the second kind. Journal of Integral Equations Applications, 14 (4), pp. 355-376.
    Chen, Z., Micchelli, C., and Xu, Y. (2001). A multilevel method for solving operator equations. Journal of Mathematical Analysis and Applications, 262, pp. 688-699.
    Micchelli, C. A., Sauer, T., and Xu, Y. (2001). Subdivision schemes for iterated function systems. Proc. Amer. Math. Soc., 129 (no. 6), pp. 186-1872.
    Kaneko, H., Padilla, P., and Xu, Y. (2001). Superconvergence of the iterated degenerate kernel method. Applicable Analysis, 80, pp. 331-351.
    Ford, W. F., Pennline, J. A., Xu, Y., and Zhao, Y. (2000). Asymptotic error analysis of a quadrature method for integral equations with Greens function kernels. Journal of Integral Equations Applications, 12, pp. 349-384.
    Dahmen, W., Schneider, R., and Xu, Y. (2000). Nonlinear Functionals of Wavelet Expansions - Adaptive Reconstruction and Fast Evaluation. Numerische Mathematik, 86 (1), pp. 49-101.
    Chen, Z., Micchelli, C., and Xu, Y. (1999). A Construction of Interpolating Wavelets on Invariant Sets. Math. Comp., 68, pp. 1569-1587.
    Chen, G., Chen, Z., and Xu, Y. (1999). Numerical Computation of a Heavily Loaded Flexible-beam Model. Comm. Numer. Methods Engineering, 15, pp. 249-261.
    Chen, Z., Xu, Y., and Zhao, J. (1999). The Discrete Petrov-Galerkin Method for Second Kind Integral Equations. Journal of Integral Equations Applications, 11, pp. 1-35.
    Micchelli, C., Sauer, T., and Xu, Y. (1998). A construction of refinable sets for interpolating wavelets. Results in Mathematics, 34, pp. 359-372.
    Xu, Y. (1998). Numerical Treatments for Boundary Integral Equations. Advances in Computational Mathematical
    Chen, Z., and Xu, Y. (1998). The Petrov-Galerkin and Iterated Petrov-Galerkin Methods for Second Kind Integral Equations. SIAM Journal on Numerical Analysis, 35, pp. 406-434.
    Bogacki, P., Weinstein, S., and Xu, Y. (1997). Distance between oriented curves in geometric modeling. Advances in Computational Math., 7, pp. 593-621.
    Chen, Z., Micchelli, C., and Xu, Y. (1997). The Petrov-Galerkin Methods for Second Kind Integral Equations II: Multiwavelet Scheme. Advances in Computational Mathematics, 7, pp. 199-233.
    Micchelli, C., Xu, Y., and Zhao, Y. (1997). Wavelet Galerkin Methods for Systems of Multivariate Integral Equations. J. Comp. Appl. Math., 86, pp. 251-270.
    Micchelli, C. A., and Xu, Y. (1997). Reconstruction and Decomposition Algorithms for Biorthogonal Multiwavelets. Multidimensional Systems and Signal Processing, 8 (1-2), pp. 31-69.
    Xu, Y., and Zhao, Y. (1996). An extrapolation method for a class of boundary integral equations. Mathematics of Computation, 65, pp. 587-610.
    Deutsch, F., Ubhaya, V., Ward, J. D., and Xu, Y. (1996). Constrained best approximation in Hilbert space III: Applications to n-convex functions. Constructive Approximation, 12, pp. 361-384.
    Ford, W. F., Xu, Y., and Zhao, Y. (1996). Derivative Correction for Quadrature Formulas. Advances in Computational Mathematics, 6, pp. 139-157.
    Xu, Y., and Zhao, Y. (1996). Quadratures for boundary integral equations of the rst kind with logarithmic kernels,. Journal of Integral Equations Applications, 8, pp. 239-268.
    Kaneko, H., and Xu, Y. (1996). Superconvergence of the iterated Galerkin methods for Hammerstein equations. SIAM Journal on Numerical Analysis, 33, pp. 1048-1064.
    Ubhaya, V., and Xu, Y. (1995). Constrained Lp-approximation by generalized n-convex functions induced by ECT systems. Journal of Approximation Theory, 80, pp. 423-449.
    Shen, Z., and Xu, Y. (1995). Degenerate kernel schemes by wavelets for nonlinear integral equations on the real line. Applicable Analysis, 59, pp. 163-184.
    Bogacki, P., Weinstein, S., and Xu, Y. (1995). Degree reduction of Bezier curves by uniform approximation with endpoint interpolation. Computer-Aided Design, 27, pp. 651-661.
    Deutsch, F., Ubhaya, V. A., and Xu, Y. (1995). Dual cones, constrained n-convex Lp-approximation and perfect splines. Journal of Approximation Theory, 80, pp. 180-203.
    Xu, Y. (1995). Recursions for Tchebyche B-splines and their jumps. NATO ASI Series, 454,
    Micchelli, C. A., and Xu, Y. (1995). Using the matrix renement equation for the construction of wavelets II: Smooth wavelets. Approximation and Computation A Festschrift in Honor of Walter Gautschi pp. 435-457.
    Hu, R., Micchelli, C., and Xu, Y. (1995). Weakly singular Fredholm integral equations II: Singularity preserving wavelet collocation methods. Approximation Theory VIII: Wavelet and Multilevel Approximation pp. 167-178.
    Xu, Y. (1995). Weakly singular Fredholm integral equations I: Singularity preserving wavelet Galerkin methods., 2, pp. 283-300.
    Ford, W. F., Xu, Y., and Zhao, Y. (1994). Extrapolation methods for nonlinear boundary integral equations. Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics pp. 1249-1252.
    Kaneko, H., and Xu, Y. (1994). Gaussian-type quadratures for weakly singular integrals and their applications to the Fredholm integral equation of the second kind. Mathematics of Computation, 62, pp. 739-753.
    Xu, Y., and Zhao, Y. (1994). Quadratures for improper integrals and their applications in integral equations. Proceedings of Symposia in Applied Mathematics, 48, pp. 409-413.
    Hu, R., Kaneko, H., and Xu, Y. (1994). Singularity preserving collocation method for weakly singular Fredholm integral equations of the second kind. Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics pp. 1311-1314.
    Cao, Y., and Xu, Y. (1994). Singularity preserving Galerkin methods for weakly singular Fredholm integral equations. Journal of Integral Equations and Applications, 6, pp. 303-334.
    Micchelli, C. A., and Xu, Y. (1994). Using the matrix refinement equation for the construction of wavelets on invariant sets. Applied and Computational Harmonic Analysis, 1, pp. 391-401.
    Kaneko, H., and Xu, Y. (1992). Degenerate kernel method for multi-variable Hammerstein equations. Applied Numerical Mathematics, 10, pp. 473-479.
    Weistein, S., and Xu, Y. (1992). Degree reduction of Bezier curves by approximation and interpolation. The Proceedings of 6th South Eastern Approximation Theorists International pp. 503-512.
    Kaneko, H., Noren, R., and Xu, Y. (1992). Numerical solutions for weakly singular Hammerstein equations and their superconvergence. Journal of Integral Equations and Applications, 4, pp. 391-407.
    Weinstein, S., and Xu, Y. (1991). A duality approach to best uniform convex approximation. Journal of Mathematical Analysis and Applications, 160, pp. 314-322.
    Swetits, J., Weinstein, S., and Xu, Y. (1991). Best Lp approximation by multiple constraints for 1 p < 1,. Journal of Approximation Theory, 65, pp. 90-108.
    Kaneko, H., and Xu, Y. (1991). Degenerate kernel method for Hammerstein equations. Mathematical of Computation, 65, pp. 141-148.
    Kaneko, H., and Xu, Y. (1991). Numerical solutions for weakly singular Fredholm integral equations of the second kind. Applied Numerical Mathematics, 7, pp. 167-177.
    Kaneko, H., Noren, R., and Xu, Y. (1990). A characterization of the solution of a Fredholm integral equation with L1 forcing term. Journal of Integral Equations and Applications, 2, pp. 581-594.
    Swetits, J., Weinstein, S., and Xu, Y. (1990). Approximation in Lp[0, 1] by n-Convex Functions,. Numerical Functional Analysis and Optimization, 11, pp. 167-179.
    Ubhaya, V., Weinstein, S., and Xu, Y. (1990). Best piecewise monotone uniform approximation. Journal of Approximation Theory, 63, pp. 375-383.
    Weinstein, S., and Xu, Y. (1990). Best quasi-convex uniform approximation. Journal of Mathemat--cal Analysis and Applications, 152, pp. 240-251.
    Swetits, J., Weistein, S., and Xu, Y. (1990). On the characterization and computation of best monotone approximation in Lp[0; 1]. Journal of Approximation Theory, 60, pp. 58-69.
    Swetits, J. J., Weinstein, S., and Xu, Y. (1990). The computation of a best monotone Lp approximation for 1 p < 1,. Numerical Functional Analysis and Optimization, 11 (7-8), pp. 811-822.
    Kaneko, H., Noren, R., and Xu, Y. (1990). Regularity of the solution of Hammerstein equations with weakly singular kernel,. Integral Equation and Operator Theory, 13 (5), pp. 660-670.
    Swetits, J., Weinstein, S., and Xu, Y. (1989). The characterization of best n-convex approximation in Lp[0; 1] for 1 p < 1,. Approximation Theory VI pp. 651-654.
    Weinstein, S., and Xu, Y. (1989). Uniform approximation by piecewise monotone functions with free knots. Approximation Theory VI pp. 671-674.
  • Books

    Chen, Z., Micchelli, C., and Xu, Y. (2015). Multiscale Methods for Fredholm Integral Equations. Cambridge University Press.
  • 2010: Excellence in Graduate Education Faculty Recognition Award,, Syracuse University.
  • 2001: Eberly Family Professor of Mathematics, West Virginia University
  • 1999: Fred Waldron Award for Excellence in Research, North Dakota State University
  • 1998: Best Researcher Award of Science and Mathematics, North Dakota State University
  • 1996: Alexander von Humboldt Research Fellow,
  • Contracts, Grants and Sponsored Research

    Xu, Y. "Research supported by NASA, NSF, DOE, DOD AND CDC" . 1996 - 2018