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arXiv · 1305.0526

Matrix Inversion Is As Easy As Exponentiation

Sushant Sachdeva·Nisheeth K. Vishnoi
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Abstract

We prove that the inverse of a positive-definite matrix can be approximated by a weighted-sum of a small number of matrix exponentials. Combining this with a previous result [OSV12], we establish an equivalence between matrix inversion and exponentiation up to polylogarithmic factors. In particular, this connection justifies the use of Laplacian solvers for designing fast semi-definite programming based algorithms for certain graph problems. The proof relies on the Euler-Maclaurin formula and certain bounds derived from the Riemann zeta function.

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Sushant Sachdeva, Nisheeth K. Vishnoi. 2013-05-02. Matrix Inversion Is As Easy As Exponentiation. https://arxiv.org/abs/1305.0526

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