Faster Deterministic Pseudoinverse-Free Block Extension of Motzkin Method for Large Consistent Linear Systems

Abstract

. Recently, a fast deterministic block Kaczmarz (FDBK) method which uses a greedy criterion of the row selections and contains pseudoinverse-free computation is presented. In this work, we introduce a maximum residual rule into FDBK and develop a new block Kaczmarz method which is also considered as a fast deterministic pseudoinverse-free block extension of Motzkin (FBEM) method. In addition, we prove that FBEM converges linearly to the unique least-norm solution of the linear systems. Furthermore, by incorporating the Polyak momentum technique into the FBEM iteration method, we establish an accelerated variant of FBEM (mFBEM) and show its global linear convergence. Numerical examples using artificial and real datasets demonstrate the effectiveness of FBEM as well as mFBEM.