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Überbestimmte Eigenwertaufgaben

  • S. Kasma
  • W. Wetterling
Part of the International Series of Numerical Mathematics book series (ISNM, volume 30)

Abstract

The application of the collocation principle to the problem of the oscillating membrane leads to eigenvalue problems Ax = λBx with rectangular matrices A and B. In analogy to systems of linear equations these eigenvalue problems are called overdetermined, and (x,λ) is defined to be a solution if the defect (A-λB)x is minimized in the sense of least squares approximation under a condition gTx = 1 or xTCx = 1. In this paper we consider a family of such problems with matrices Ar and Br continuously differentiable with respect to a real variable r. Under suitable assumptions existence of a solution and convergence of an iterative method can be proved using the implicit function theorem.

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Literatur

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Copyright information

© Springer Basel AG 1976

Authors and Affiliations

  • S. Kasma
    • 1
  • W. Wetterling
    • 1
  1. 1.Technische Hogeschool TwenteEnschede-DrienerloNiederlande

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