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arXiv · 1408.4230

Fast Approximate Matrix Multiplication by Solving Linear Systems

Shiva Manne·Manjish Pal
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Abstract

In this paper, we present novel deterministic algorithms for multiplying two $n \times n$ matrices approximately. Given two matrices $A,B$ we return a matrix $C'$ which is an \emph{approximation} to $C = AB$. We consider the notion of approximate matrix multiplication in which the objective is to make the Frobenius norm of the error matrix $C-C'$ arbitrarily small. Our main contribution is to first reduce the matrix multiplication problem to solving a set of linear equations and then use standard techniques to find an approximate solution to that system in $\tilde{O}(n^2)$ time. To the best of our knowledge this the first examination into designing quadratic time deterministic algorithms for approximate matrix multiplication which guarantee arbitrarily low \emph{absolute error} w.r.t. Frobenius norm.

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Shiva Manne, Manjish Pal. 2014-08-19. Fast Approximate Matrix Multiplication by Solving Linear Systems. https://arxiv.org/abs/1408.4230

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