All reports by Author Francois Le Gall:

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TR17-036
| 22nd February 2017
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Dean Doron, Francois Le Gall, Amnon Ta-Shma#### Probabilistic logarithmic-space algorithms for Laplacian solvers

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TR14-154
| 20th November 2014
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Andris Ambainis, Yuval Filmus, Francois Le Gall#### Fast Matrix Multiplication: Limitations of the Laser Method

Dean Doron, Francois Le Gall, Amnon Ta-Shma

A recent series of breakthroughs initiated by Spielman and Teng culminated in the construction of nearly linear time Laplacian solvers, approximating the solution of a linear system $L x=b$, where $L$ is the normalized Laplacian of an undirected graph. In this paper we study the space complexity of the problem.

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Andris Ambainis, Yuval Filmus, Francois Le Gall

Until a few years ago, the fastest known matrix multiplication algorithm, due to Coppersmith and Winograd (1990), ran in time $O(n^{2.3755})$. Recently, a surge of activity by Stothers, Vassilevska-Williams, and Le Gall has led to an improved algorithm running in time $O(n^{2.3729})$. These algorithms are obtained by analyzing higher ... more >>>