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Schur Decomposition Methods for the Computation of Rational Matrix Functions

  • T. Politi
  • M. Popolizio
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3994)

Abstract

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 − z j I)y = b.

Keywords

Rational Approximation Matrix Function Partial Fraction Krylov Subspace Chebyshev Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • T. Politi
    • 1
  • M. Popolizio
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di BariBariItaly
  2. 2.Dipartimento di MatematicaUniversità degli Studi di BariBariItaly

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