Topics in matrix analysis
Approximation of matrix-valued functions
SIAM Journal on Matrix Analysis and Applications
Compututational Techniques for Real Logarithms of Matrices
SIAM Journal on Matrix Analysis and Applications
Conditioning and Padé Approximation of the Logarithm of a Matrix
SIAM Journal on Matrix Analysis and Applications
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Evaluating Padé Approximants of the Matrix Logarithm
SIAM Journal on Matrix Analysis and Applications
A Schur-Parlett Algorithm for Computing Matrix Functions
SIAM Journal on Matrix Analysis and Applications
Exponentials of skew-symmetric matrices and logarithms of orthogonal matrices
Journal of Computational and Applied Mathematics
Hi-index | 0.00 |
In this paper we give bounds for the error arising in the approximation of the logarithm of a block triangular matrix T by Pade 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.