Matrix Inversion Is As Easy As Exponentiation
نویسندگان
چکیده
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 [6], 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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ورودعنوان ژورنال:
- CoRR
دوره abs/1305.0526 شماره
صفحات -
تاریخ انتشار 2013