An EM based Iterative Method for Solving Large Sparse Linear Systems

TL;DR

This paper introduces an EM-based iterative algorithm for efficiently solving large sparse linear systems, guaranteeing convergence under certain conditions and demonstrating competitive performance.

Contribution

The paper presents a new EM-based iterative method for large sparse linear systems, with proven convergence properties and ease of implementation.

Findings

Guaranteed convergence for systems with a unique solution

Convergence to a minimal KL divergence point otherwise

Competitive performance with existing algorithms

Abstract

We propose a novel iterative algorithm for solving a large sparse linear system. The method is based on the EM algorithm. If the system has a unique solution, the algorithm guarantees convergence with a geometric rate. Otherwise, convergence to a minimal Kullback--Leibler divergence point is guaranteed. The algorithm is easy to code and competitive with other iterative algorithms.