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A direct iteration method of obtaining latent roots and vectors of a symmetric matrix

Published online by Cambridge University Press:  24 October 2008

A. Jennings
A. Jennings
Affiliation:
Department of Civil Engineering, Queen's University, Belfast
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Abstract

This paper describes a method whereby iteration can be carried out simultaneously with two or more trial vectors in order to obtain the latent roots of largest modulus of a symmetric matrix and their corresponding latent vectors. The convergence of any particular vector is automatically accelerated by making use of the current approximations to those vectors subdominant to it, the dominant latent vectors being obtained quite rapidly. The method is particularly suitable where a few of the dominant latent roots and vectors are required of a large symmetric matrix.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 755 - 765
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Aitken, A. C.The evaluation of the latent roots and vectors of a matrix. Proc. Roy. Soc. Edinburgh Sect. A 57 (1937), 269–304.Google Scholar
(2)Duncan, W. J. and Collar, A. R.Matrices applied to the motions of damped systems. Philos. Mag. Ser. 7, 19 (1935), 197.CrossRefGoogle Scholar
(3)Wilkinson, J. H.The calculation of the latent roots and vectors of matrices on the pilot model of the A.C.E. Proc. Cambridge Philos. Soc. 50 (1954), 536–566.CrossRefGoogle Scholar
(4)Givens, W.A method of computing eigen values and eigen vectors suggested by classical results on symmetric matrices. U.S. Bur. Stand. Appl. Math. Ser. 29 (1953), 117–122.Google Scholar
(5)Househoulder, A. S. and Bauer, F. L.On certain methods for expanding the characteristic polynomial. Numer. Math. 1 (1959), 29–37.CrossRefGoogle Scholar
(6)Crandall, S. H.Iterative procedures related to relaxation methods for eigen value problems. Proc. Roy. Soc. London Ser. A 207 (1951).Google Scholar
(7)Argyris, J. H. and Kelsey, S.Energy theorems and structural analysis (Butterworth and Co., 1960).CrossRefGoogle Scholar