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XIII.—Studies in Practical Mathematics. VI. On the Factorization of Polynomials by Iterative Methods*

Published online by Cambridge University Press:  14 February 2012

A. C. Aitken
A. C. Aitken
Affiliation:
Mathematical Institute, University of Edinburgh.
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Synopsis

The method of iteration of penultimate remainders, introduced by S. N. Lin for approximating by stages to the exact factors of a polynomial, is subjected to theoretical analysis. The matrix governing the iterative process is obtained, and its latent roots and latent vectors are found. Incidental theorems yielding further factorizations are proved, and processes are developed for accelerating convergence. Numerical examples illustrate varying situations likely to arise in practice.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 63 , Issue 2 , 1951 , pp. 174 - 191
Copyright
Copyright © Royal Society of Edinburgh 1951

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References

REFERENCES TO LITERATURE

Aitken, A. C., 1926. Proc. Roy. Soc. Edin., XLVI, 289–305.Google Scholar
Aitken, A. C., 1931. Proc. Roy. Soc. Edin., LI, 80–90.Google Scholar
Aitken, A. C., 1937. Proc. Roy. Soc. Edin., LVII, 269–304.Google Scholar
Friedman, B., 1949. Comm. Pure and Appl. Math., 11, 195–208.CrossRefGoogle Scholar
Fry, T. C., 1945. Quart. Appl. Math., III, 89.CrossRefGoogle Scholar
Lin, S. N., 1941. Journ. Appl. Math. and Phys., xx, 231–241. (The method outlined here seems to have been first used in a thesis submitted for the degree of Sc.D. to the M.I.T. in 1939.)Google Scholar
Steffensen, J. F., 1933. Skand. Akt.-Tidskr., 64–72.Google Scholar
Whittaker, E. T., and Robinson, G., 1929. The Calculus of Observations, 2nd Ed., 79–83, 106.Google Scholar