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Mathematical Problems in Engineering
Volume 2017, Article ID 1375716, 8 pages
Research Article

Vector Extrapolation Based Landweber Method for Discrete Ill-Posed Problems

1School of Mathematical Sciences/Research Center for Image and Vision Computing, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
2School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, China
3Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Nijenborgh 9, P.O. Box 407, 9700 AK Groningen, Netherlands

Correspondence should be addressed to Xian-Ming Gu; nc.evil@gnimnaixug

Received 10 June 2017; Revised 12 September 2017; Accepted 18 September 2017; Published 16 November 2017

Academic Editor: Qingling Zhang

Copyright © 2017 Xi-Le Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Landweber method is one of the classical iterative methods for solving linear discrete ill-posed problems. However, Landweber method generally converges very slowly. In this paper, we present the vector extrapolation based Landweber method, which exhibits fast and stable convergence behavior. Moreover, a restarted version of the vector extrapolation based Landweber method is proposed for practical considerations. Numerical results are given to illustrate the benefits of the vector extrapolation based Landweber method.