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姓名： 王海永
性别： 男
出生日期： 1983-09-23
职位： 副教授
电话：
Email： haiyongwang@hust.edu.cn
个人主页：
基本情况Basic
教育背景Educational backgroundPh.D. in Mathematics, 09/2007—12/2010School of Mathematics and StatisticsCentral South UniversityChangsha, 410083Hunan ProvinceSupervisor: Professor Shuhuang XiangB.Sc. in Mathematics, 09/2001—06/2005School of Mathematics and StatisticsCentral South UniversityChangsha, 410073Hunan Province
工作经历Work experienceAssociate Professor in Mathematics, 01/2013—presentSchool of Mathematics and StatisticsHuazhong University of Science and TechnologyWuhan, 430074Hubei ProvincePostdoc research fellow, 03/2011—12/2012Department of Computer ScienceUniversity of LeuvenCelestijnenlaan 200A, 3001 LeuvenBelgium
研究方向Research fields1. Numerical methods for highly oscillatory problemsStarting 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. QuadratureGauss 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 methodsSpectral 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 interpolationBarycentric 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.
科研成果Scientific achievementsPublications:1、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 2、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, 20143、Wang Haiyong, Zhang Lun and Huybrechs Daan, Asymptotic expansions and fast computation of oscillatory Hilbert transforms, Numerische Mathematik, 123 (4),709—743, 20134、Wang Haiyong and Xiang Shuhuang, On the convergence rates of Legendre approximation, Mathematics of Computation, 81 (278), 861—877, 20125、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, 20116、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, 20117、Xiang Shuhuang and Wang Haiyong, Fast integration of highly oscillatory integrals with exotic oscillators, Mathematics of Computation, 79 (270), 829—844, 20108、Xiang Shuhuang, Chen Xiaojun and Wang Haiyong, Error bounds for approximation in Chebyshev points, Numerische Mathematik, 116 (3), 463—491, 20109、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, 201010、Wang Haiyong and Xiang Shuhuang, Uniform approximations to Cauchy principal value integrals of oscillatory functions, Applied Mathematics and Computation, 215 (5), 1886—1894, 200911、Xiang Shuhuang and Wang Haiyong, On the Levin iterative methods for oscillatory integrals, Journal of Computational and Applied Mathematics, 217 (1), 38—45, 2008Preprints:1. Wang Haiyong and Huybrechs Daan, Fast and accurate computation of Jacobi expansion coefficients of analytic functions, arXiv:1404.2463, 20142. Wang Haiyong, Convergence rate and acceleration of Clenshaw-Curtis quadrature for functions with endpoint singularities, arXiv:1401.0638, 2014.
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