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IV.—Studies in Practical Mathematics. V. On the Iterative Solution of a System of Linear Equations*

Published online by Cambridge University Press:  14 February 2012

A. C. Aitken
A. C. Aitken
Affiliation:
Mathematical Institute, 16 Chambers Street, Edinburgh, 1.
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Synopsis

The convergence of customary processes of iteration for solving linear equations, in particular simple and Seidelian iteration, is studied from the standpoint of matrices. A new variant of Seidelian iteration is introduced. In the positive definite case it always converges, the characteristic roots of its operator being real and positive and less than unity.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 63 , Issue 1 , 1950 , pp. 52 - 60
Copyright
Copyright © Royal Society of Edinburgh 1950

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References

References to Literature

Aitken, A. C., 1925. “On Bernoulli's Numerical Solution of Algebraic Equations”, Proc. Roy. Soc. Edin., XLVI, 289–305.Google Scholar
Aitken, A. C., 1937. “The Evaluation of the Latent Roots and Latent Vectors of a Matrix”, Proc. Roy. Soc. Edin., LVII, 269–304.Google Scholar
Bodewig, E., 1947. “Bericht über die verschieden Methoden zur Lösung eines System linearer Gleichungen mit reellen Koeffizienten”, Indag. Math., IX, 441–452 1104–1116, 1285–1295; x, 53–64, 211–219.Google Scholar
Frazer, R. A., Duncan, W. J., and Collar, A. R., 1938. Elementary Matrices, Cambridge University Press.CrossRefGoogle Scholar
Steffensen, J. F., 1933. “Remarks on Iteration”, Skandinavisk Aktuarietidskr., 64–72.Google Scholar
Turnbull, H. W., and Aitken, A. C., 1932. Theory of Canonical Matrices, Blackie & Son, London and Glasgow.Google Scholar
Whittaker, E. T., and Robinson, G., 1924. The Calculus of Observations, Blackie & Son, London and Glasgow.Google Scholar