AN APPLICABLE APPROXIMATION METHOD AND ITS APPLICATION

doi:10.1016/S0252-9602(15)30048-5

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (5): 1189-1202.doi: 10.1016/S0252-9602(15)30048-5

AN APPLICABLE APPROXIMATION METHOD AND ITS APPLICATION

Huaixin CAO¹, Zhengli CHEN¹, Li LI², Baomin YU³

1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China;
2. School of Sciences, Xi'an Polytechnic University, Xi'an 710048, China;
3. College of Mathematics and Information Science, Weinan Normal University, Weinan 714000, China

收稿日期:2013-07-03 修回日期:2015-03-06 出版日期:2015-09-01 发布日期:2015-09-01
作者简介:Huaixin CAO, E-mail: caohx@snnu.edu.cn; Zhengli CHEN, E-mail: czl@snnu.edu.cn; Li LI, E-mail: lilian6263@163.com; Baomin YU, E-mail: bmyuu@hotmail.com
基金资助:
This work was partial support by the NSFC (11371012, 11401359, 11471200), the FRF for the Central Universities (GK201301007), and the NSRP of Shaanxi Province (2014JQ1010).

AN APPLICABLE APPROXIMATION METHOD AND ITS APPLICATION

Huaixin CAO¹, Zhengli CHEN¹, Li LI², Baomin YU³

1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China;
2. School of Sciences, Xi'an Polytechnic University, Xi'an 710048, China;
3. College of Mathematics and Information Science, Weinan Normal University, Weinan 714000, China

Received:2013-07-03 Revised:2015-03-06 Online:2015-09-01 Published:2015-09-01
Supported by:
This work was partial support by the NSFC (11371012, 11401359, 11471200), the FRF for the Central Universities (GK201301007), and the NSRP of Shaanxi Province (2014JQ1010).

摘要/Abstract

摘要：

In this work, by choosing an orthonormal basis for the Hilbert space L²[0,1], an approximation method for finding approximate solutions of the equation (I+K)x=y is proposed, called Haar wavelet approximation method (HWAM). To prove the applicability of the HWAM, a more general applicability theorem on an approximation method (AM) for an operator equation Ax=y is proved first. As an application, applicability of the HWAM is obtained. Furthermore, four steps to use the HWAM are listed and three numerical examples are given in order to illustrate the effectiveness of the method.

关键词: Hilbert space, applicability, Haar wavelet, approximation method, operator equation

Abstract:

Key words: Hilbert space, applicability, Haar wavelet, approximation method, operator equation

中图分类号:

47A58

Huaixin CAO, Zhengli CHEN, Li LI, Baomin YU. AN APPLICABLE APPROXIMATION METHOD AND ITS APPLICATION[J]. 数学物理学报(英文版), 2015, 35(5): 1189-1202.

Huaixin CAO, Zhengli CHEN, Li LI, Baomin YU. AN APPLICABLE APPROXIMATION METHOD AND ITS APPLICATION[J]. Acta mathematica scientia,Series B, 2015, 35(5): 1189-1202.

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AN APPLICABLE APPROXIMATION METHOD AND ITS APPLICATION

AN APPLICABLE APPROXIMATION METHOD AND ITS APPLICATION

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