A Note on the Use of the Woodbury Formula To Solve Cyclic Block Tri-Diagonal and Cyclic Block Penta-diagonal Linear Systems of Equations

TL;DR

This paper discusses algorithms for solving cyclic block tridiagonal and penta-diagonal linear systems using the Woodbury formula, providing theoretical insights into their implementation.

Contribution

It offers a theoretical framework for applying the Woodbury formula to cyclic block systems, enhancing understanding of these algorithms.

Findings

Theoretical basis for using Woodbury formula in cyclic block systems

Algorithms for cyclic block tridiagonal and penta-diagonal systems

Insights into algorithmic implementation and efficiency

Abstract

The article presents the theoretical background of the algorithms for solving cyclic block tridiagonal and cyclic block penta-diagonal systems of linear algebraic equations present in ref [1] and [2]. The theory is based on the Woodbury formula.