# Recursive Matrix Algorithms in Commutative Domain for Cluster with Distributed Memory

## TL;DR

This paper reviews theoretical matrix algorithms in commutative domains, presents experimental results on parallel implementations on a supercomputer, and demonstrates their scalability and efficiency for distributed memory clusters.

## Contribution

It introduces new parallel matrix algorithms in commutative domains and evaluates their scalability and efficiency on a supercomputer cluster.

## Key findings

- Algorithms achieve high efficiency on distributed memory clusters
- Parallel programs scale well with increasing processors
- Applications include various computational tasks in algebra and matrix computations

## Abstract

We give an overview of the theoretical results for matrix block-recursive algorithms in commutative domains and present the results of experiments that we conducted with new parallel programs based on these algorithms on a supercomputer MVS-10P at the Joint Supercomputer Center of the Russian Academy of Science. To demonstrate a scalability of these programs we measure the running time of the program for a different number of processors and plot the graphs of efficiency factor. Also we present the main application areas in which such parallel algorithms are used. It is concluded that this class of algorithms allows to obtain efficient parallel programs on clusters with distributed memory.