Year: 2024
Type: article
Abstract: What is the largest constant α such that for all ɛ > 0, an n × n and n×nα matrices can be multiplied in O(n2+ε)? Coppersmith (1982) was the first to present a lower bound on α, showing that α≥0.172. Coppersmith further proposes a second proof that leads to the bound α≥0.1402, and combined with a newer construction by Coppersmith and Winograd (1982), the second bound improves to α≥0.197. We revisit this work, show that the second proof is incorrect, and propose an alternative one. Our alternative proof uses a recursive construction, based on the Schönhage’s multiplication stacking technique, that converges to the same bound on α.
Source: Research in Mathematics
Authors: Roy Nissim, Oded Schwartz
Institution: Hebrew University of Jerusalem
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Funder: European Research Council
OpenAlex ID: W4401709455