报告人：向淑晃（中南大学）

报告题目：On Approximation and Its Approximatinos: Gauss versus Chebyshev, and Lagrange versus Hermite-Fejer

报告摘要：Along the way to Bernstein (1912), Fejer (1933), Curtis and Rabinowitz (1972), Riess and Johnson (1972), Trefethen (2008, 2013) etc., by building on the aliasing errors on integration of Chebyshev polynomials and using the asymptotic formulae on the coefficients of Chebyshev expansions, in this presentation, we will consider optimal general convergence rates for n-point Gauss, Clenshaw-Curtis and Fejer’s first and second rules for Jacobi weights. All are of approximately equal accuracy. The convergence rate of these quadrature rules is up to one power of n better than polynomial best approximation. Further, we will introduce the optimal general convergence rates for Lagrange interpolation polynomials deriving from Gauss or Chebyshev points, and fast implementation of these polynomials by barycentric formulae. In addition, we will compare Lagrange interpolation with Hermilte-Fejer interpolation for continuous functions. Finally, we consider some applications in acoustic scattering problems.

报告人简介：向淑晃，中南大学教授、数学与统计学院院长。从事函数逼近，高振荡问题数值方法、矩阵理论与计算等研究，在SIAM J. Numer. Anal.、SIAM J. Optimization、SIAM J. Sci. Comput.、Math. Program A、Numer. Math.、Math. Comp、IMA J. Numer. Anal.等计算数学知名期刊发表论文九十余篇，主持国家自然基金多项。

报告时间：2018年6月2日（星期六）上午8:40-9:30

报告地点：科技楼南702