Algorithms for Recursive Block Matrices

TL;DR

This paper explores algorithms for recursive block matrices, focusing on inversion and triangular decomposition, with applications to matrices over rings that are neither real nor complex, highlighting both practical and theoretical benefits.

Contribution

It introduces new algorithms for block matrix inversion and triangular decomposition, extending previous results to matrices over more general rings.

Findings

Efficient algorithms for block matrix inversion

Triangular decomposition methods for recursive block matrices

Extension of inversion techniques to non-real, non-complex rings

Abstract

We study certain linear algebra algorithms for recursive block matrices. This representation has useful practical and theoretical properties. We summarize some previous results for block matrix inversion and present some results on triangular decomposition of block matrices. The case of inverting matrices over a ring that is neither formally real nor formally complex was inspired by Gonzalez-Vega et al.