A fast multiscale Galerkin method for the first kind ill-posed integral equations via Tikhonov regularization

Authors:
Zhongying Chen;Sirui Cheng;Gnaneshwar Nelakanti;Hongqi Yang
Affiliations:
Department of Scientific Computing and Computer Applications, Sun Yat-Sen University, Guangzhou, People's Republic of China;Department of Scientific Computing and Computer Applications, Sun Yat-Sen University, Guangzhou, People's Republic of China;Department of Mathematics, Indian Institute of Technology, Kharagpur, West Bengal, India;Department of Scientific Computing and Computer Applications, Sun Yat-Sen University, Guangzhou, People's Republic of China
Venue:
International Journal of Computer Mathematics
Year:
2010

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Abstract

In this paper, we develop a fast multiscale Galerkin method to solve the Fredholm integral equations of the first kind via Tikhonov regularization. The method leads to fast solutions of discrete regularization methods. We obtain optimal convergence rates for approximate solutions with an a priori parameter choice and a kind of discrepancy principle. Finally, numerical experiments are given to illustrate the efficiency of the method.