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.
This work was supported in part by the Dutch National Applied Science Foundation under grant FOM DEL 77.1260.
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Dedicated to I. Gohberg on the occasion of his 60th birthday.
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© 1989 Birkhäuser Verlag Basel
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Nelis, H., Dewilde, P., Deprettere, E. (1989). Inversion of Partially Specified Positive Definite Matrices by Inverse Scattering. In: Dym, H., Goldberg, S., Kaashoek, M.A., Lancaster, P. (eds) The Gohberg Anniversary Collection. Operator Theory: Advances and Applications, vol 40. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9276-6_13
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DOI: https://doi.org/10.1007/978-3-0348-9276-6_13
Publisher Name: Birkhäuser Basel
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