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Theoretical and numerical considerations about Padé approximants for the matrix logarithm |
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| Authors: | J R Cardoso F Silva Leite |
| Institution: | a Instituto Superior de Engenharia de Coimbra, Quinta da Nora, 3030 Coimbra, Portugal b Departamento de Matemática, Universidade de Coimbra, 3000 Coimbra, Portugal |
| Abstract: | We show that for a vast class of matrix Lie groups, which includes the orthogonal and the symplectic, diagonal Padé approximants of log((1+x)/(1−x)) are structure preserving. The conditioning of these approximants is analyzed. We also present a new algorithm for the Briggs–Padé method, based on a strategy for reducing the number of square roots in the inverse scaling and squaring procedure. |
| Keywords: | P-orthogonal groups Matrix logarithms Padé approximants Condition number |
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