Solving an operator equation by iteration

Spain, P. G. (1978) Solving an operator equation by iteration. Linear Algebra and its Applications, 20(1), pp. 69-70. (doi:10.1016/0024-3795(78)90030-7)

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Abstract

It was shown by Bushell [1] that the equation t′xt = x2 has a unique positive-definite solution when t is a real invertible matrix; the proof utilizes the Hilbert projective metric and the Banach fixed-point theorem. I present a simpler proof of a more general result.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Spain, Dr Philip
Authors: Spain, P. G.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Linear Algebra and its Applications
Publisher:Elsevier B.V.
ISSN:0024-3795
ISSN (Online):1873-1856

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