A randomized block extended Kaczmarz method with hybrid partitions for solving large inconsistent linear systems

Abstract

We propose a randomized block extended Kaczmarz method with hybrid partitioning techniques for solving large inconsistent linear systems. It employs the k-means clustering to partition the columns of the coefficient matrix while applying the uniform sampling to derive the row partition of the coefficient matrix. It is proved that the proposed algorithm converges to the unique least-squares least-norm solution in expectation. Numerical examples validate that the new algorithm is competitive when compared with other randomized extended Kaczmarz-type methods.