Article

GSTF Journal of Mathematics, Statistics and Operations Research (JMSOR)

, 4:9

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

GKB-GCV Method for Solving Generic Tikhonov Regularization Problems

  • Dai TogashiAffiliated withGraduate School of Science and Technology, Keio University
  • , Takashi NoderaAffiliated withDepartment of Mathematics, Keio University

Abstract

The W-GCV method is one of the iterative methods used to solve a large scale Vtandard form of the Tikhonov regularization, but it is also necessary for solving the general form of the Tikhonov regularization. This paper proposes a new solver, called GKB-GCV, which is an extension of the W-GCV by using the GSVD. Numerical results are presented to show the usefulness of the GKB-GCV method in large scale ill-posed problems.

Keywords-

GKB W-GCV Tikhonov regularization large scale ill-posed problem Image resolution