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学术报告四十三:On Approximation and Its Approximatinos: Gauss versus Chebyshev

来源:数学与统计学院     作者:     时间:2018/6/7 10:59:18  0次

数学与统计学院学术报告[2018] 043

 (高水平大学建设系列报告162)

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

报告人:  向淑晃 教授  中南大学

报告时间:201867日下午3:20—4:20

报告地点: 科技楼514

报告内容:Along the way to Bernstein (1912), Fej′er (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 Fej′er’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-Fej′er interpolation for continuous functions. Finally, we consider some applications in acoustic scattering problems.

报告人简历:中南大学教授、博士生导师、数学与统计学院院长,主要从事高振动问题数值方法、正交多项式逼近理论、高效计算等研究,在SIAM J. Numer. Anal.SIAM J. Sci. Comput.SIAM J. OptimizationMath. Program ANumer. Math.Math. CompIMA J. Numer. Anal.Adv. Comput. Math.等国际计算数学顶级期刊发表系列论文,主持国家自然基金多项, 2006年入选教育部新世纪优秀人才计划,2011年入选湖南省学了带头人培养对象。

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