A generalized global Arnoldi method for ill-posed matrix equations


This paper discusses the solution of large-scale linear discrete ill-posed problems with a noise-contaminated right-hand side. Tikhonov regularization is used to reduce the influence of the noise on the computed approximate solution. We consider problems in which the coefficient matrix is the sum of Kronecker products of matrices and present a generalized global Arnoldi method, that respects the structure of the equation, for the solution of the regularized problem. Theoretical properties of the method are shown and applications to image deblurring are described.

DOI: 10.1016/j.cam.2011.09.031

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@article{Bouhamidi2012AGG, title={A generalized global Arnoldi method for ill-posed matrix equations}, author={Abderrahman Bouhamidi and Khalide Jbilou and Lothar Reichel and Hassane Sadok}, journal={J. Computational Applied Mathematics}, year={2012}, volume={236}, pages={2078-2089} }