A partially block randomized extended Kaczmarz method for solving large overdetermined inconsistent linear systems

Abstract

This paper presents a partial block randomized extended Kaczmarz (PBREK) method for solving large overdetermined inconsistent linear system of equations $ Ax = b $. The convergence theorem of the PBREK method is derived. Several examples are given to illustrate the effectiveness of the proposed PBREK method compared with the prevuious PREK method and the randomized extended Kaczmarz (REK) method.

Keywords

• partial block randomized extended kaczmarz
• overdetermined inconsistent systems
• matrix paving
• kaczmarz method