Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (5): 1189-1202.doi: 10.1016/S0252-9602(15)30048-5

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AN APPLICABLE APPROXIMATION METHOD AND ITS APPLICATION

Huaixin CAO1, Zhengli CHEN1, Li LI2, Baomin YU3   

  1. 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).

Abstract:

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.

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

CLC Number: 

  • 47A58
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