Computing

, Volume 3, Issue 4, pp 268–279 | Cite as

On the orthonormalization of sparse vectors

  • R. P. Tewarson
Article

Summary

The problem of finding the optimum order in which the columns of a given sparse matrix should be orthonormalized, such that the resulting matrix is as sparse as possible, is discussed. It is shown how, under certain conditions, the optimum can be determined. Some computationally simple methods, which give a reasonably close approximation to the optimum column order, are given. The results of computational experiments performed on randomly generated matrices are also given. The analysis and the results of the paper hold for both theGram-Schmidt and theHouseholder methods of orthonormalization.

Keywords

Computational Mathematic Computational Experiment Close Approximation Optimum Order Sparse Matrix 

Zusammenfassung

Wir betrachten das folgende Problem: Wie soll die optimale Ordnung der Spalten einer gegebenen sparse Matrize orthonormalisiert werden, so daß die sich ergebende Matrize so sparse wie möglich ist. Es wird gezeigt wie unter gewissen Bedingungen das Optimum bestimmt werden kann. Verschiedene Methoden sind gegeben, welche vom Berechnungsstandpunkt aus einfach sind, und welche eine ziemlich genaue Annäherung an die optimale Spaltenordnung geben. Die Resultate der Berechnungsexperimente, die mit zufällig erzeugten Matrizen durchgeführt wurden, sind auch angegeben. Die Analyse und die Resultate dieser Arbeit gelten für dieGram-Schmidt und auch für dieHouseholdersche Orthonormalisierungsmethode.

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Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • R. P. Tewarson
    • 1
  1. 1.State University of New YorkStony BrookUSA

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