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Numerical aspects of the generalized CG-method applied to least squares problems

Numerische Aspekte der Anwendung des verallgemeinerten CG-Verfahrens auf Least-Squares-Probleme

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Abstract

The Generalized Conjugate Gradient (GCG) method of Concus and Golub [1] and Widlund [2] and its adjusted form (AGCG) are considered for the numerical solution of the least squares problems. Some numerical comparisons with the SOR [3] and CG [4] method are also given indicate that the GCG method is always better than the SOR [3] and that the adjusted GCG (AGCG) scheme is preferable to the CG, GCG and SOR methods.

Zusammenfassung

Die verallgemeinerte Methode der konjugierten Gradienten (GCG) von Concus und Golub [1] und Widlund [2] und ihre angepaßte Form (AGCG) werden bei der numerischen Lösung von Least-Squares-Problemen untersucht. Einige numerische Vergleiche mit dem SOR-Verfahren [3] und dem CG-Verfahren [4] werden gezogen und deuten an, daß die GCG-Methode stets besser als die SOR-Methode ist und daß das AGCG-Schema allen anderen erwähnten Methoden vorzuziehen ist.

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References

  1. Concus, P., Golub, G. H.: A generalized conjugate gradient method for nonsymmetric systems of linear equations. Lecture Notes in Economics and Mathematical Systems 134 (Glowinski, R., Lions, J. L., eds.), pp. 56–65. New York: Springer-Verlag 1976.

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  2. Widlund, O.: A Lanczos method for a class of nonsymmetric systems of linear equations. SIAM Numer. Anal.15, 801–812 (1978).

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  4. Freund, R.: A note on two block SOR method for sparse least squares problems. LAA88/89, 211–221 (1987).

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Authors and Affiliations

  1. Department of Computer Studies, Loughborough University of Technology, Le11 3TU, Leicestershire, UK

    D. J. Evans & C. Li

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  1. D. J. Evans
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  2. C. Li
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Evans, D.J., Li, C. Numerical aspects of the generalized CG-method applied to least squares problems. Computing 41, 171–178 (1989). https://doi.org/10.1007/BF02238742

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  • DOI: https://doi.org/10.1007/BF02238742

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