Date of Award

6-2023

Document Type

Open Access

Department

Computer Science

Second Department

Mathematics

First Advisor

Matthew Anderson

Second Advisor

Jeffrey Hatley

Language

English

Keywords

Computational Complexity, Matrix Multiplication, Group Theory, Linear Algebra, Abstract Algebra, Ring Theory, Wedderburn, Artin, Computational Group Theory, Theory, Theoretical Computer Science, Complexity Theory, Bremner, Ivanyos, Ronyai, Friedl, GAP, Sage, Semisimple Algebra, Semisimple Ring, Artinian Ring, Wedderburn Decomposition, Cohn and Umans, SUSP, Uniquely Solvable Puzzles, Matt Anderson, Jeff Hatley

Abstract

Researchers Cohn and Umans proposed a framework for fast matrix multiplication algorithms. Their approach is reliant on an application of the Wedderburn-Artin Theorem: a landmark classification result in modern algebra. We show experimental success for algebras whose components all have dimension 1. We advance the Cohn and Umans framework by developing new, extendable tools to couple with their design.

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Rights Statement

In Copyright - Educational Use Permitted.