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On the fill-in when sparse vectors are orthonormalized

Über die Füllung wenn magere Vektoren orthonormalisiert werden

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Summary

If the RevisedGram-Schmidt method is used for orthonormalizing a given set of sparse vectors, then it is shown that the local fill-in of non-zero elements at each stage can be easily determined. This makes it possible to rearrange the remaining vectors at each stage such that the local fill-in is minimized. It is also shown that a similar method can also be used in the case of theHouseholder triangularization method.

Zusammenfassung

Wenn die revidierteGram-Schmidt-Methode in der Orthonormalisierung einer gegebenen Menge magerer Vektoren angewendet wird, so kann die lokale Füllung von Nicht-Null-Elementen bei jedem Schrift leicht bestimmt werden. Dies ermöglicht eine Neuordnung der verbleibenden Vektoren bei jedem Schrift, die dann eine möglichst kleine lokale Füllung ergibt. Es wird hier ferner gezeigt, daß eine ähnliche Methode auch im Fall derHouseholder-Triangulisierungsmethode verwendet werden kann.

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References

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Authors and Affiliations

  1. Applied Mathematics and Statistics Department, State University of New York, 11790, Stony Brook, NY, U.S.A.

    Y. T. Chen &  R. P. Tewarson

Authors
  1. Y. T. Chen
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  2. R. P. Tewarson
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Chen, Y.T., Tewarson, R.P. On the fill-in when sparse vectors are orthonormalized. Computing 9, 53–56 (1972). https://doi.org/10.1007/BF02236376

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  • DOI: https://doi.org/10.1007/BF02236376

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