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- W2615970112 abstract "Two algorithms are developed for computing the matrix logarithm in floatingpoint arithmetic of any specified precision. The backward error-basedapproach used in the state of the art inverse scaling and squaringalgorithms does not conveniently extend to a multiprecision environment, soinstead we choose algorithmic parameters based on a forward error bound. Wederive a new forward error bound for Pad'{e} approximants that forhighly nonnormal matrices can be much smaller than the classical bound ofKenney and Laub. One of our algorithms exploits a Schur decompositionwhile the other is transformation-free and uses only the computationalkernels of matrix multiplication and the solution of multiple right-handside linear systems. For double precision computations the algorithms arecompetitive with the state of the art algorithm of Al-Mohy, Higham, andRelton implemented in texttt{logm} in MATLAB@. They are intended forcomputing environments providing multiprecision floating point arithmetic,such as Julia, MATLAB via the Symbolic Math Toolbox or the MultiprecisionComputing Toolbox, or Python with the mpmath or SymPy packages. We showexperimentally that the algorithms behave in a forward stable manner over awide range of precisions, unlike existing alternatives." @default.
- W2615970112 created "2017-05-26" @default.
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- W2615970112 date "2018-01-01" @default.
- W2615970112 modified "2023-10-12" @default.
- W2615970112 title "Multiprecision Algorithms for Computing the Matrix Logarithm" @default.
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- W2615970112 doi "https://doi.org/10.1137/17m1129866" @default.
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