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2012•Journal of Inverse and Ill-Posed ProblemsRequires access

A fast multiscale Galerkin method for ill-posed integral equations with not exactly given input data via Tikhonov regularization

Xingjun Luo, Yang Xu, Huang Xian-tong, Fanchun Li

Open publisher page 6 citations

Abstract

Abstract. In this paper we develop a fast multiscale Galerkin method solving ill-posed integral equations with not exactly given input data via Tikhonov regularization. The method leads to fast solutions of discrete Tikhonov regularization. The convergence rates of the Tikhonov regularization are achieved by using a modified discrepancy principle. Finally, numerical experiments are given to illustrate the efficiency of the method.

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What this paper is about

Abstract. In this paper we develop a fast multiscale Galerkin method solving ill-posed integral equations with not exactly given input data via Tikhonov regularization. The method leads to fast solutions of discrete Tikhonov regularization. The convergence rates of the Tikhonov regularization are achieved by using a modified discrepancy principle. Finally, numerical experiments are given to illustrate the efficiency of the method.

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Available abstract

Abstract. In this paper we develop a fast multiscale Galerkin method solving ill-posed integral equations with not exactly given input data via Tikhonov regularization. The method leads to fast solutions of discrete Tikhonov regularization. The convergence rates of the Tikhonov regularization are achieved by using a modified discrepancy principle. Finally, numerical experiments are given to illustrate the efficiency of the method.

Key concepts: Tikhonov regularization, Regularization (linguistics), Backus–Gilbert method, Galerkin method, Mathematics, Regularization perspectives on support vector machines, Applied mathematics, Integral equation

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