Modular Analysis of Almost Block Diagonal Systems of Equations

TL;DR

This paper presents a modular analysis framework for almost block diagonal systems, enabling the development and assessment of various elimination methods, including new ones, with a focus on efficiency and stability.

Contribution

It introduces a modular approach to analyze and construct elimination methods for almost block diagonal systems, including new methods and a robust partial pivoting strategy.

Findings

Six existing elimination methods analyzed

Fourteen new elimination methods proposed

Robust local pivoting strategy developed

Abstract

Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of the methods on the basis of their operation counts, storage needs, and admissibility of partial pivoting. It unveils a robust partial pivoting strategy- local pivoting. Extension of modular analysis to bordered systems is also included.