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arXiv

New error bounds for Legendre approximations of differentiable functions

作     者:Wang, Haiyong 

作者机构:School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China 

出 版 物:《arXiv》 (arXiv)

年 卷 期:2021年

核心收录:

主  题:Error analysis 

摘      要:In this paper we present a new perspective on error analysis for Legendre approximations of differentiable functions. We start by introducing a sequence of Legendre-Gauss-Lobatto polynomials and prove their theoretical properties, including an explicit and optimal upper bound. We then apply these properties to derive a new explicit bound for the Legendre coefficients of differentiable functions. Building on this, we establish an explicit and optimal error bound for Legendre approximations in the L2 norm and an explicit and optimal error bound for Legendre approximations in the L∞ norm under the condition that their maximum error is attained in the interior of the interval. Illustrative examples are provided to demonstrate the sharpness of our new results. Copyright © 2021, The Authors. All rights reserved.

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