Parallel Factorizations in Numerical Analysis

TL;DR

This paper reviews parallel factorization methods for solving sparse linear systems, especially those from discretized differential equations, highlighting efficient parallel extensions and a unified approach to solving ODEs.

Contribution

It introduces a unifying framework for parallel matrix factorizations, enhancing the efficiency of solving sparse linear systems from ODE discretizations.

Findings

Efficient parallel algorithms for block tridiagonal matrices.

Unified approach to parallel solution of ODEs.

Improved computational performance in numerical analysis.

Abstract

In this paper we review the parallel solution of sparse linear systems, usually deriving by the discretization of ODE-IVPs or ODE-BVPs. The approach is based on the concept of parallel factorization of a (block) tridiagonal matrix. This allows to obtain efficient parallel extensions of many known matrix factorizations, and to derive, as a by-product, a unifying approach to the parallel solution of ODEs.