Optimal control as a regularization method for ill-posed problems

被引：0

作者：

Department of Mathematics, UCLA, United States ^{[1
]}

不详 ^{[2
]}

不详 ^{[3
]}

机构：

来源：

J Inverse Ill Posed Probl | 2006年 / 7卷 / 685-703期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1515/156939406779802022

中图分类号：

学科分类号：

摘要：

We describe two regularization techniques based on optimal control for solving two types of ill-posed problems. We include convergence proofs of the regularization method and error estimates. We illustrate our method through problems in signal processing and parameter identification using an efficient Riccati solver. Our numerical results are compared to the same examples solved using Tikhonov regularization. © VSP 2006.

引用

共 50 条

[41] Regularization of weakly ill-posed Cauchy problems
Melnikova, I.V.
Zheng, Q.
Zhang, J.
Journal of Inverse and Ill-Posed Problems, 2003, 10 (05):
[42] OPTIMALITY IN THE REGULARIZATION OF ILL-POSED INVERSE PROBLEMS
DAVIES, AR
HASSAN, MF
ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS, 1987, : 553 - 562
[43] Regularization for ill-posed parabolic evolution problems
Fury, Matthew A.
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2012, 20 (5-6): : 667 - 699
[44] REGULARIZATION OF ILL-POSED PROBLEMS BY PROJECTION METHODS
NATTERER, F
NUMERISCHE MATHEMATIK, 1977, 28 (03) : 329 - 341
[45] Tikhonov regularization for nonlinear ill-posed problems
Hou, ZY
Jin, QN
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 28 (11) : 1799 - 1809
[46] DISCRETE REGULARIZATION OF OPTIMAL-CONTROL PROBLEMS ON ILL-POSED MONOTONE VARIATIONAL-INEQUALITIES
LISKOVETS, OA
MATHEMATICS OF THE USSR-IZVESTIYA, 1990, 54 (05): : 321 - 335
[47] Application of the method of regularization to solve ill-posed problems of coordinate measurements
V. P. Suslin
A. V. Dzhunkovskii
Measurement Techniques, 2009, 52 : 719 - 724
[48] Optimal discretization of Ill-posed problems
S. V. Pereverzev
S. G. Solodkii
Ukrainian Mathematical Journal, 2000, 52 (1)
[49] An Iterative Multigrid Regularization Method for Toeplitz Discrete Ill-Posed Problems
Donatelli, Marco
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2012, 5 (01) : 43 - 61
[50] A novel iterative integration regularization method for ill-posed inverse problems
Huang, Ce
Wang, Li
Fu, Minghui
Lu, Zhong-Rong
Chen, Yanmao
ENGINEERING WITH COMPUTERS, 2021, 37 (03) : 1921 - 1941

← 1 2 3 4 5 →