Matrix Inversion Is As Easy As Exponentiation
Data Structures and Algorithms
2016-08-23 v2 Numerical Analysis
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.
Cite
@article{arxiv.1305.0526,
title = {Matrix Inversion Is As Easy As Exponentiation},
author = {Sushant Sachdeva and Nisheeth K. Vishnoi},
journal= {arXiv preprint arXiv:1305.0526},
year = {2016}
}
Comments
This paper appears in the monograph 'Faster Algorithms via Approximation Theory' written by the authors