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Experiments on orthogonalization by biorthogonal representations of orthogonal projectors

By Miroslav Andrle and Laura Rebollo-Neira

Abstract

AbstractA number of experiments are performed with the aim of enhancing a particular feature arising when biorthogonal sequences are used for the purpose of orthogonalization. It is shown that an orthogonalization process executed by biorthogonal sequences and followed by a re-orthogonalization step admits four numerically different realizations. The four possibilities are originated by the fact that, although an orthogonal projector is by definition a self-adjoint operator, due to numerical errors in finite precision arithmetic the biorthogonal representation does not fulfil such a property. In the experiments presented here one of the realizations is shown clearly numerically superior to the remaining three

Publisher: Elsevier B.V.
Year: 2007
DOI identifier: 10.1016/j.cam.2006.05.029
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