Padé approximation for the exponential of a block triangular matrix
The problem of computing the exponential of a block triangular matrix via Padé approximation techniques is examined, where the blocks themselves are not necessarily triangular. The main result in the paper gives improved error bounds, both absolute and relative, when the matrix is \(2 \times 2\) with well scaled diagonal blocks. This yields a new scaling and squaring technique for such matrices as well as its corresponding error analysis. The new strategy produces satisfactory approximations, mainly by avoiding the problem of overscaling. The extension of the results to block triangular matrices with more than two diagonal blocks appears to be a straightforward matter.
scientific article; zbMATH DE number 1446351