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Numerische Mathematik

, Volume 60, Issue 1, pp 115–131 | Cite as

Smooth factorizations of matrix valued functions and their derivatives

  • Peter Kunkel
  • Volker Mehrmann
Article

Summary

In this paper we study the numerical factorization of matrix valued functions in order to apply them in the numerical solution of differential algebraic equations with time varying coefficients. The main difficulty is to obtain smoothness of the factors and a numerically accessible form of their derivatives. We show how this can be achieved without numerical differentiation if the derivative of the given matrix valued function is known. These results are then applied in the numerical solution of differential algebraic Riccati equations. For this a numerical algorithm is given and its properties are demonstrated by a numerical example.

Mathematics Subject Classification (1991)

65L02 65F25 93C15 93B40 

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Peter Kunkel
    • 1
  • Volker Mehrmann
    • 2
  1. 1.Fachbereich MathematikUniversität OldenburgOldenburgFederal Republic of Germany
  2. 2.Institut für Geometrie und praktische MathematikRWTH AachenAachenFederal Republic of Germany

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