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Exploring Arbitrary Precision Approximate Matrix Multiplication
Algebra & Discrete Mathematics| Speaker: | Ryan Schneider, UC Berkeley |
| Related Webpage: | https://sites.google.com/view/ryan-schneider-math?pli=1&authuser=0 |
| Location: | 2112 MSB |
| Start time: | Mon, Nov 9 2026, 4:10PM |
Description
Arbitrary Precision Approximate (APA) matrix multiplication describes a family of algorithms that generalize matrix multiplication. An APA routine takes input matrices $A$ and $B$ and outputs their exact product plus a small remainder term, which depends on $A$ and $B$ and an evaluation parameter $\varepsilon$. Importantly, it is possible to (1) compute the exact product $AB$ from an APA routine and (2) do so asymptotically faster than any exact algorithm. Moreover, each APA algorithm corresponds to a border rank decomposition of the matrix multiplication tensor. Despite all of this, APA matrix multiplication has remained somewhat overlooked in the literature. In this talk, I'll revisit these algorithms with the goal of exploring their theoretical and numerical properties.