Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
Incomplete partial fractions for parallel evaluation of rational matrix functions
Journal of Computational and Applied Mathematics
Computer-controlled systems (3rd ed.)
Computer-controlled systems (3rd ed.)
A Schur-Parlett Algorithm for Computing Matrix Functions
SIAM Journal on Matrix Analysis and Applications
Analysis of Projection Methods for Rational Function Approximation to the Matrix Exponential
SIAM Journal on Numerical Analysis
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In this work we consider the problem to compute the vector $y={\it \Phi}_{m,n}(A)x$ where ${\it \Phi}_{m,{\it n}}$(z) is a rational function, x is a vector and A is a matrix of order N, usually nonsymmetric. The problem arises when we need to compute the matrix function f(A), being f(z) a complex analytic function and ${\it \Phi}_{m,{\it n}}$(z) a rational approximation of f. Hence ${\it \Phi}_{m,{\it n}}$(A) is a approximation for f(A) cheaper to compute. We consider the problem to compute first the Schur decomposition of A then the matrix rational function exploting the partial fractions expansion. In this case it is necessary to solve a sequence of linear systems with the shifted coefficient matrix (A−zjI)y=b.