In this work we consider the problem to compute the vector y=Φm,n(A)x where Φm,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 Φm,n(z) a rational approximation of f. Hence Φm,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 − z j I)y = b.

Schur Decomposition Methods for the Computation of Rational Matrix Functions / Politi, T.; Popolizio, M.. - STAMPA. - 3994:(2006), pp. 708-715. (Intervento presentato al convegno 6th International Conference on Computational Science, ICCS 2006 tenutosi a Reading, UK nel May 28-31, 2006) [10.1007/11758549_96].

Schur Decomposition Methods for the Computation of Rational Matrix Functions

T. Politi;M. Popolizio
2006-01-01

Abstract

In this work we consider the problem to compute the vector y=Φm,n(A)x where Φm,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 Φm,n(z) a rational approximation of f. Hence Φm,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 − z j I)y = b.
2006
6th International Conference on Computational Science, ICCS 2006
978-3-540-34385-1
Schur Decomposition Methods for the Computation of Rational Matrix Functions / Politi, T.; Popolizio, M.. - STAMPA. - 3994:(2006), pp. 708-715. (Intervento presentato al convegno 6th International Conference on Computational Science, ICCS 2006 tenutosi a Reading, UK nel May 28-31, 2006) [10.1007/11758549_96].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/17615
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