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Numerische Mathematik

, Volume 23, Issue 2, pp 99–104 | Cite as

On a geometrical aspect of SOR and the theory of consistent ordering for positive definite matrices

  • R. A. Nicolaides
Article

Abstract

On the basis of a similarity transformation of ℒω, the successive overrelaxation operator, a geometrical interpretation of SOR is given. It is shown how the theory of consistent ordering falls into the resulting framework and how connections between SOR and other algorithms can be established.

Keywords

Mathematical Method Similarity Transformation Geometrical Interpretation Geometrical Aspect Positive Definite Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Bodewig, E.: Matrix Calculus. Amsterdam: North-Holland Publishing Company 1956Google Scholar
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    Hotelling, H.: Am. Math. Stat.14, 1–34 (1943)Google Scholar
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    Kacmarcz, S.: Bull. Intern. Acad. Pol. Sci. A, 1937, p. 355–357Google Scholar
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    Nicolaides, R. A.: On the numerical solution of quasilinear elliptic equations. Ph. D. thesis, London University, 1972Google Scholar
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    Varga, R. S.: Matrix Interative Analysis. New Jersey: Prentice Hall 1962Google Scholar
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    Young, D. M.: Iterative solution of large linear systems. New York: Academic Press, 1971Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • R. A. Nicolaides
    • 1
  1. 1.Department of Applied MathematicsCalifornia Institute of TechnologyPasadenaUSA

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