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Krylov iterative methods for the geometric mean of two matrices times a vector

Authors
  • Castellini, Jacopo1
  • 1 Università degli Studi di Perugia, Via Vanvitelli 1, Perugia, 06123, Italy , Perugia (Italy)
Type
Published Article
Journal
Numerical Algorithms
Publisher
Springer US
Publication Date
Jun 11, 2016
Volume
74
Issue
2
Pages
561–571
Identifiers
DOI: 10.1007/s11075-016-0161-4
Source
Springer Nature
Keywords
License
Yellow

Abstract

In this work, we are presenting an efficient way to compute the geometric mean of two positive definite matrices times a vector. For this purpose, we are inspecting the application of methods based on Krylov spaces to compute the square root of a matrix. These methods, using only matrix-vector products, are capable of producing a good approximation of the result with a small computational cost.

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