Ph.D. in Mathematics, 09/2007 — 12/2010 School of Mathematics and Statistics Central South University Changsha, 410083 Hunan Province Supervisor: Professor Shuhuang Xiang B.Sc. in Mathematics, 09/2001 — 06/2005 School of Mathematics and Statistics Central South University Changsha, 410073 Hunan Province
Associate Professor in Mathematics, 01/2013 — present School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan, 430074 Hubei Province Postdoc Research Fellow, 03/2011 — 12/2012 Department of Computer Science University of Leuven Celestijnenlaan 200A, 3001 Leuven Belgium
1. Numerical methods for highly oscillatory problems Starting from my PhD, I am interested in efficient methods for highly oscillatory integrals such as numerical steepest descent methods, Filon-type methods and Levin-type methods. 2. Quadrature Gauss and Clenshaw-Curtis quadrature are two improtant methods for computing integrals numerically. Their convergence rates for various functions are of interest. Especially, I am interested in convergence rate and acceleration of Clenshaw-Curtis quadrature for singular functions. 3. Spectral methods Spectral expansions in terms of Jacobi, Legendre and Chebyshev polynomials are widely used in solving differential equations. Typically, these expansion coefficients can not be calculated exactly and numerical algorithms should be developed to provide approximation. I am interested in developing fast and accurate methods for the computation of Jacobi coefficients. Meanwhile, I am also interested in the optimal estimatie of these spectral expansion coefficients. 4.Barycentric interpolation Barycentric interpolation formula is a fast and stable method for computing the polynomial interpolant numerically. In practice, most attention is paid to the Chebyshev roots and extreme points. Here, I am interested in the Legendre and Jacobi points and explicit barycentric weights for these points are given which enables us to evaluate the corresponding polynomial interpolants efficiently.
Publications: 14. Wang Haiyong and Huybrechs Daan, Fast and accurate computation of Chebyshev coefficients in the complex plane, IMA Journal of Numerical Analysis, to appear, 2016. 13. Wang Haiyong, On the optimal estimates and comparison of Gegenbauer expansion coefficients, SIAM Journal on Numerical Analysis, 54(3), 1557–1581, 2016 12. Wang Haiyong, Huybrechs Daan and Vandewalle Stefan, Explicit barycentric weights for polynomial interpolation in the roots or extrema of classical orthogonal polynomials, Mathematics of Computation, 83 (290), 2893—2914, 2014 11. Asheim Andreas, Deano Alfredo, Huybrechs Daan and Wang Haiyong, A Gaussian quadrature rule for oscillatory integrals on a bounded interval, Discrete and Continuous Dynamical Systems A, 34 (3), 883—901, 2014 10. Xiang Shuhuang, He Guo and Wang Haiyong, On fast and stable implementation of Clenshaw-Curtis and Fejér-type quadrature rules, Abstract and Applied Analysis, Volume 2014, Article ID 436164, 2014 9. Wang Haiyong, Zhang Lun and Huybrechs Daan, Asymptotic expansions and fast computation of oscillatory Hilbert transforms, Numerische Mathematik, 123 (4), 709—743, 2013 8. Wang Haiyong and Xiang Shuhuang, On the convergence rates of Legendre approximation, Mathematics of Computation, 81 (278), 861—877, 2012 7. Xiang Shuhuang, Cho Yeol Je, Wang Haiyong and Brunner Hermann, Clenshaw-Curtis-Filon-type methods for highly oscillatory Bessel transforms and applications, IMA Journal of Numerical Analysis, 31 (4), 1281—1314, 2011 6. Wang Haiyong and Xiang Shuhuang, Asymptotic expansion and Filon-type methods for a Volterra integral equation with a highly oscillatory kernel, IMA Journal of Numerical Analysis, 31 (2), 469—490, 2011 5. Xiang Shuhuang and Wang Haiyong, Fast integration of highly oscillatory integrals with exotic oscillators, Mathematics of Computation, 79 (270), 829—844, 2010 4. Xiang Shuhuang, Chen Xiaojun and Wang Haiyong, Error bounds for approximation in Chebyshev points, Numerische Mathematik, 116 (3), 463—491, 2010 3. Wang Haiyong and Xiang Shuhuang, On the evaluation of Cauchy principal value integrals of oscillatory functions, Journal of Computational and Applied Mathematics, 234 (1), 95—100, 2010 2. Wang Haiyong and Xiang Shuhuang, Uniform approximations to Cauchy principal value integrals of oscillatory functions, Applied Mathematics and Computation, 215 (5), 1886—1894, 2009 1. Xiang Shuhuang and Wang Haiyong, On the Levin iterative methods for oscillatory integrals, Journal of Computational and Applied Mathematics, 217 (1), 38—45, 2008 Preprints: 1. Wang Haiyong and Huybrechs Daan, Fast and accurate computation of Jacobi expansion coefficients of analytic functions, arXiv:1404.2463, 2014 2. Wang Haiyong, Convergence rate and acceleration of Clenshaw-Curtis quadrature for functions with endpoint singularities, arXiv:1401.0638, 2014. 3. Wang Haiyong and Zhang Lun, Jacobi polynomials on the Bernstein ellipse, arXiv:1703.04243, 2017.
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