Inversion of Partially Specified Positive Definite Matrices by Inverse Scattering

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


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.


Block Matrix Positive Definite Matrix Positive Definite Matrice Triangular Part Approximate Inverse 
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© Birkhäuser Verlag Basel 1989

Authors and Affiliations

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

There are no affiliations available

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