Fasi, Massimiliano and Iannazzo, Bruno (2020) The dual inverse scaling and squaring algorithm for the matrix logarithm. [MIMS Preprint] (Unpublished)
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Abstract
The inverse scaling and squaring algorithm computes the logarithm of a square matrix A by evaluating a rational approximant to the logarithm at the matrix B:=A^{2^{s}} for a suitable choice of s. We introduce a dual approach and approximate the logarithm of B by solving the rational equation r(X)=B, where r is a diagonal Padé approximant to the matrix exponential at 0. This equation is solved by a substitution technique in the style of those developed in (Fasi & Iannazzo, Elect. Trans. Num. Anal., 53 (2020), pp. 500521). The new method is tailored to the special structure of the diagonal Padé approximants to the exponential, and in terms of computational cost is more efficient than the stateoftheart inverse scaling and squaring algorithm.
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:  15 May 2021 07:21 
Last Modified:  15 May 2021 07:21 
URI:  https://eprints.maths.manchester.ac.uk/id/eprint/2810 
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The dual inverse scaling and squaring algorithm for the matrix logarithm. (deposited 27 May 2020 09:27)
 The dual inverse scaling and squaring algorithm for the matrix logarithm. (deposited 15 May 2021 07:21) [Currently Displayed]
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