Experiments on orthogonalization by biorthogonal representations of orthogonal projectors

Miroslav Andrle, Laura Rebollo-Neira*

*Corresponding author for this work

Research output: Contribution to journalLetter, comment or opinionpeer-review


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.

Original languageEnglish
Pages (from-to)545-551
Number of pages7
JournalJournal of Computational and Applied Mathematics
Issue number1
Publication statusPublished - 1 Aug 2007


  • Biorthogonal basis
  • Gram-Schmidt orthogonalization
  • Orthogonal projections
  • Re-orthogonalization


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