Padé and Gregory error estimates for the logarithm of block triangular matrices
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-transf...
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| Format: | article |
| Language: | eng |
| Published: |
2006
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| Online Access: | http://hdl.handle.net/10316/4619 |
| Country: | Portugal |
| Oai: | oai:estudogeral.sib.uc.pt:10316/4619 |
| Summary: | 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. |
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