Computing the weighted geometric mean of two large-scale matrices and its inverse times a vector

Fasi, Massimiliano and Iannazzo, Bruno (2016) Computing the weighted geometric mean of two large-scale matrices and its inverse times a vector. [MIMS Preprint]

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Abstract

We investigate different approaches for computing the action of the weighted geometric mean of two large-scale positive definite matrices on a vector. We derive and analyze several algorithms, based on numerical quadrature and on the Krylov subspace, and compare them in terms of convergence speed and execution time. By exploiting an algebraic relation between the weighted geometric mean and its inverse, we show how these methods can be used to efficiently solve large linear systems whose coefficient matrix is a weighted geometric mean. According to our experiments, some of the algorithms proposed in both families are suitable choices for black-box implementations.

Item Type:	MIMS Preprint
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Mr Massimiliano Fasi
Date Deposited:	21 Jul 2017
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2561

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• Computing the weighted geometric mean of two large-scale matrices and its inverse times a vector. (deposited 22 May 2016)
  • Computing the weighted geometric mean of two large-scale matrices and its inverse times a vector. (deposited 21 Jul 2017) [Currently Displayed]

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