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Title: Padé and Gregory error estimates for the logarithm of block triangular matrices
Authors: Cardoso, João R. 
Silva Leite, F. 
Keywords: Matrix logarithm; Inverse scaling and squaring; Padé approximants and Gregory's series
Issue Date: 2006
Citation: Applied Numerical Mathematics. 56:2 (2006) 253-267
Abstract: In this paper we give bounds for the error arising in the approximation of the logarithm of a block triangular matrix T by Padé approximants of the function f(x)=log[(1+x)/(1-x)] and partial sums of Gregory's series. These bounds show that if the norm of all diagonal blocks of the Cayley-transform B=(T-I)(T+I)-1 is sufficiently close to zero, then both approximation methods are accurate. This will contribute for reducing the number of successive square roots of T needed in the inverse scaling and squaring procedure for the matrix logarithm.
DOI: 10.1016/j.apnum.2005.04.003
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Internacionais

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