Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4646419 | Applied Numerical Mathematics | 2006 | 15 Pages |
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)−1(T+I) 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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