Regularization methods for a problem of analytic continuation

被引：7

作者：

Xiong, Xiangtuan ^{[1
]}

Zhu, Liqin ^{[1
]}

Li, Ming ^{[1
]}

机构：

[1] Taiyuan Univ Technol, Dept Math, Taiyuan, Shanxi, Peoples R China

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2011年 / 82卷 / 02期

基金：

中国国家自然科学基金; 高等学校博士学科点专项科研基金;

关键词：

Analytic continuation; Ill-posed problems; Generalized Tikhonov regularization; Stability estimate; Error estimate; ILL-POSED PROBLEMS; GENERAL SOURCE CONDITIONS; CONDITIONAL STABILITY; HEAT-EQUATION; CONTINUITY; MODULUS;

D O I：

10.1016/j.matcom.2011.08.005

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, we prove a sharp stability estimate for the problem of analytic continuation. Based on the obtained stability estimate, a generalized Tikhonov regularization is provided and the corresponding error estimate is obtained. Moreover, we give many other regularization methods. For illustration, a numerical experiment is constructed to demonstrate the feasibility and efficiency of the proposed method. (C) 2011 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：332 / 345

页数：14

共 22 条

[1]

[Anonymous], 1977, NEW YORK

[2]

Engl H. W., 1996, REGULARIZATION INVER

[3] A MODIFIED TIKHONOV REGULARIZATION FOR STABLE ANALYTIC CONTINUATION [J].

Fu, Chu-Li ;

Deng, Zhi-Liang ;

Feng, Xiao-Li ;

Dou, Fang-Fang .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (04) :2982-3000

[4] A simple regularization method for stable analytic continuation [J].

Fu, Chu-Li ;

Dou, Fang-Fang ;

Feng, Xiao-Li ;

Qian, Zhi .

INVERSE PROBLEMS, 2008, 24 (06)

[5]

Hao D., 1998, Methods for inverse heat conduction problems.-Peter Lang pub

[6] A MOLLIFICATION METHOD FOR ILL-POSED PROBLEMS [J].

HAO, DN .

NUMERISCHE MATHEMATIK, 1994, 68 (04) :469-506

[7]

HAO DN, 2004, P ICAM HANOI, V14, P3

[8] Modulus of continuity for conditionally stable ill-posed problems in Hilbert space [J].

Hofmann, B. ;

Mathe, P. ;

Schieck, M. .

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2008, 16 (06) :567-585

[9] Impact of conditional stability: Convergence rates for general linear regularization methods [J].

Kabanikhin, S. I. ;

Schieck, M. .

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2008, 16 (03) :267-282

[10]

Murio D.A., 1993, The Mollification Method and the Numerical Solution of Ill-Posed Problems

← 1 2 3 →