Weaker assumptions for convergence of extended block Kaczmarz and Jacobi projection algorithms

Abstract

Recent developments in the field of image reconstruction have given rise to the use of projective iterative methods, such as Kaczmarz and Jacobi, when solving inconsistent linear least squares problems. In this paper we try to generalize previous results concerning extended block versions of these two algorithms. We replace the inverse operator with the Moore-Penrose pseudoinverse and try to prove convergence under weaker assumptions. In order to accomplish this task, we show that these algorithms are special cases of a general iterative process for which convergence is already established.

Keywords

• inconsistent linear least squares problem
• extended block kaczmarz algorithm
• extended block jacobi with relaxation parameters algorithm
• moore-penrose pseudoinverse
• clustering
• 65f10
• 65f20