Applications of Haar basis method for solving some ill-posed inverse problems

被引：16

作者：

Pourgholi, R. ^{[1
]}

Tavallaie, N. ^{[1
]}

Foadian, S. ^{[1
]}

机构：

[1] Damghan Univ, Sch Math & Comp Sci, Damghan, Iran

来源：

JOURNAL OF MATHEMATICAL CHEMISTRY | 2012年 / 50卷 / 08期

关键词：

Ill-posed inverse problems; Haar basis method; Tikhonov regularization method; Noisy data; GENERALIZED CROSS-VALIDATION; HEAT-CONDUCTION; WAVELET METHOD;

D O I：

10.1007/s10910-012-0036-4

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

In this paper a numerical method consists of combining Haar basis method and Tikhonov regularization method for solving some ill-posed inverse problems using noisy data is presented. By using a sensor located at a point inside the body and measuring the u(x, t) at a point x = a, 0 < a < 1, and applying Haar basis method to the inverse problem, we determine a stable numerical solution to this problem. Results show that an excellent estimation on the unknown functions of the inverse problem can be obtained within a couple of minutes CPU time at pentium IV-2.4 GHz PC.

引用

页码：2317 / 2337

页数：21

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