Experiments on orthogonalization by biorthogonal representations of orthogonal projectors |
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Authors: | Miroslav Andrle Laura Rebollo-Neira |
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Institution: | Aston University, Birmingham, B4 7ET, UK |
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Abstract: | A 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. |
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Keywords: | Biorthogonal basis Orthogonal projections Gram&ndash Schmidt orthogonalization Re-orthogonalization |
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