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Inversion of Partially Specified Positive Definite Matrices by Inverse Scattering

  • H. Nelis
  • P. Dewilde
  • E. Deprettere
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 40)

Abstract

Inverse scattering techniques such as the Wiener-Hopf factorization and the Schur algorithm can be used to determine an approximate inverse of a partially specified positive definite matrix. In this paper we explore the connection between inverse scattering and matrix extension theory from a mathematical and algorithmic point of view. We present fast algorithms for computing either the exact inverse of the maximum entropy extension of a partially specified positive definite matrix or a close approximation to it, depending on the structure of the set on which the matrix is specified. We aim at presenting a unification of various results which have appeared in the literature and present some new results as well.

Keywords

Block Matrix Positive Definite Matrix Positive Definite Matrice Triangular Part Approximate Inverse 
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

© Birkhäuser Verlag Basel 1989

Authors and Affiliations

  • H. Nelis
  • P. Dewilde
  • E. Deprettere

There are no affiliations available

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