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On computing generalized inverses

Zur Berechnung verallgemeinerter Inverser

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Summary

A method for computing the generalized inverse of a matrix is described, which makes use of elementary orthogonal matrices and theGaussian elimination. The method also yields orthonormal bases for the ranges and the null spaces of the matrix and the generalized inverse. Modifications of the method for the solution of simultaneous linear equations are given. Compact storage schemes, in the case of sparse matrices, are also described.

Zusammenfassung

In der vorliegenden Arbeit wird eine Methode zur Berechnung der verallgemeinerten Inversen einer Matrix beschrieben. Diese Methode verwendet elementare, orthogonale Matrizen und dieGausssche Elimination. Sie liefert auch orthogonale Grundlagen für die Reichweiten und die Nullräume der Matrix und ihrer verallgemeinerten Inversen. Modifikationen der Methode zur Lösung von simultanen linearen Gleichungen werden gegeben. Überdies werden kompakte Lagerungsschemen im Falle von spärlichen Matrizen beschrieben.

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Authors and Affiliations

  1. State University of New York, 11790, Stony Brook, N. Y., USA

    Reginald P. Tewarson (Associate Professor)

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  1. Reginald P. Tewarson
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With 1 Figure

This work was supported in part by the National Aeronautics and Space Administration under Grant NGR-33-015-013.

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Tewarson, R.P. On computing generalized inverses. Computing 4, 139–152 (1969). https://doi.org/10.1007/BF02234761

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  • DOI: https://doi.org/10.1007/BF02234761

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