Interpolation and Expansion on Orthogonal Polynomials

        發布者:文明辦作者:發布時間:2020-12-21瀏覽次數:10


        主講人:向淑晃  中南大學教授


        時間:2020年12月21日10:00


        地點:騰訊會議 936 571 594


        舉辦單位:數理學院


        主講人介紹:向淑晃,中南大學二級教授、博士生導師,2006年入選教育部新世紀優秀人才計劃,2011年入選湖南省學科帶頭人培養計劃,2019年4月至今擔任湖南省計算數學與應用軟件學會理事長。主要從事正交多項式逼近的快速、高精度算法以及高頻振蕩問題高效計算與收斂性研究。在SIAM  J. Numer. Anal.、SIAM J. Optimization、SIAM Sci. Comput.、Math. Program A、Numer.  Math.、Math.  Comput.、BIT等國內外核心期刊發表論文100余篇,其中SCI、EI收錄100余篇。主持國家自然科學基金面上項目4項、湖南省自然基金面上項目、湖南省自然基金重點項目、教育部留學基金各1項。2004年獲日本JSPS振興學會資助,日本國立大學弘前大學長期特邀研究員,現為美國《Mathematical  Reviews》、德國《Zentralblatt Math》評論員、湖南省計算數學與應用軟件學會理事長、《Information》雜志編委。


        內容介紹:The convergence rates on polynomial interpolation in most cases are estimated by  Lebesgue constants. These estimates may be overestimated for some special points  of sets for functions of limited regularities. In this talk, new formulas on the  convergence rates are considered. Moreover, new and optimal asymptotics on the  coefficients of functions of limited regularity expanded in forms of Jacobi and  Gegenbauer polynomial series are presented. All of these asymptotic analysis are  optimal. Numerical examples illustrate the perfect coincidence with the  estimates.

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