Legendre Polynomials-Based Numerical Differentiation: A Convergence Analysis in a Weighted L2 Space
Legendre Polynomials-Based Numerical Differentiation: A Convergence Analysis in a Weighted L~2 Space作者机构：College of Information and Engineering Dalian University School of Mathematical Sciences Dalian University of Technology
出 版 物：《Journal of Mathematical Research with Applications》 (数学研究及应用(英文版))
年 卷 期：2016年第36卷第2期
页 面：247-252页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：Supported by the National Nature Science Foundation of China(Grant Nos.11301052 11301045 11401077 11271060 11290143) the Fundamental Research Funds for the Central Universities(Grant No.DUT15RC(3)058) the Fundamental Research of Civil Aircraft(Grant No.MJ-F-2012-04)
主 题：Legendre polynomials numerical differentiation Jacobi polynomials weighted L2 space
摘 要：We consider the problem of estimating the derivative of a function f from its noisy version fδby using the derivatives of the partial sums of Fourier-Legendre series of f. Instead of the observation Lspace, we perform the reconstruction of the derivative in a weighted Lspace. This takes full advantage of the properties of Legendre polynomials and results in a slight improvement on the convergence order. Finally, we provide several numerical examples to demonstrate the efficiency of the proposed method.
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