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Computing the Matrix Sign and Absolute Value Functions

Abstract : We present two algorithms for the computation of the matrixsign and absolute value functions.Both algorithms avoid a complete diagonalisation of thematrix, but they however require some informations regarding the eigenvalues location.The first algorithm consists in a sequence of polynomial iterations based on appropriate estimates of the eigenvalues, andconverging to the matrix sign if all the eigenvalues are real.Convergence is obtained within a finite number of steps when the eigenvalues are exactly known.Nevertheless, we present a second approach for the computation of the matrix sign and absolute value functions, when the eigenvalues are exactly known.This approach is based on the resolution of an interpolation problem, can handle the case of complex eigenvalues and appears to be faster than the iterative approach.
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https://hal-cea.archives-ouvertes.fr/cea-02355780
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Submitted on : Friday, November 8, 2019 - 2:03:01 PM
Last modification on : Tuesday, April 28, 2020 - 11:28:13 AM

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M. Ndjinga. Computing the Matrix Sign and Absolute Value Functions. Comptes Rendus Mathématique, Elsevier Masson, 2008, 1, ⟨10.1016/j.crma.2007.11.028⟩. ⟨cea-02355780⟩

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