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Preprint 34-2003

A Newton method for the numerical solution of procrustes problems in finite dimensional indefinite scalar product spaces

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Author(s) : Ulric Kintzel

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 34-2003

MSC 2000

15A63 Quadratic and bilinear forms, inner products
49M15 Methods of Newton-Raphson, Galerkin and Ritz types

Abstract :
A Newton method is introduced for solving procrustes problems in finite dimensional indefinite scalar product spaces. This involves optimisation tasks for determining isometries, with the help of which two given tuples of vectors can be transformed in the sense of an optimum compensation. The sums of squared distances as well as the sums of squared areas are minimised as criterion for the compensation.

Keywords : Indefinite scalar products, procrustes problems, Newton's method

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