Professor

Mathematics & Statistics

#### Yuesheng Xu

2300 ENGR & COMP SCI BLDG

NORFOLK, 23529

**Ph.D.** in Computational Applied Math, Old Dominion University, (1989)

## Contracts, Grants and Sponsored Research

- Xu, Y. "Collaborative Research: Sparse Optimization for Machine Learning and Image/Signal Processing" $171,089. Federal. 2022 - 2025
- "Advanced Planar Image Reconstruction for Targeted Alpha Therapy" $145,173. Federal. 2022 - 2024
- "Collaborative Research: Sparse Optimization in Large Scale Data Processing: A Multiscale Proximity Approach" $125,000. Federal. 2019 - 2023
- "International Conference of Mathematics on Data Science" $15,000. Federal. 2018 - 2019

## 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. - 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. - Feiglin, D., Krol, A., Li, S., Schmidtlein, C. Ross., 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. - 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. - 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 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 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 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.

- 2020: Distinguished Research Award, College of Sciences, Old Dominion University
- 2010: Excellence in Graduate Education Faculty Recognition Award, Syracuse University
- 2001: Eberly Chair 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, German Alexander von Humboldt Foundation