The dual inverse scaling and squaring algorithm for the matrix logarithm

Fasi, Massimiliano and Iannazzo, Bruno (2020) The dual inverse scaling and squaring algorithm for the matrix logarithm. [MIMS Preprint]

Text faia20.pdf Download (297kB)

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^(1/2^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 algorithm in the style of [M. Fasi and B. Iannazzo, MIMS EPrint 2019.8, 2019] which is tailored to the special structure of the approximants to the exponential. In terms of floating-point operations, the resulting method is cheaper than the state-of-the-art 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:	27 May 2020 09:27
Last Modified:	27 May 2020 09:27
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2766

Available Versions of this Item

• The dual inverse scaling and squaring algorithm for the matrix logarithm. (deposited 27 May 2020 09:27) [Currently Displayed]
  • The dual inverse scaling and squaring algorithm for the matrix logarithm. (deposited 15 May 2021 07:21)

Actions (login required)

View Item