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XII.—Further Numerical Studies in Algebraic Equations and Matrices

Published online by Cambridge University Press:  15 September 2014

A. C. Aitken
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Extract

In a former paper on the same subject the writer pointed out that the sequence used by D. Bernoulli for approximating to the greatest root of an algebraic equation could be further utilised in such a way as to give all the roots. It is suggested in the present paper that there is really no need to compute a first Bernoullian sequence at all, but that by the theory of dual symmetric functions the coefficients in the given equation may be used with equal convenience. In a practical respect this simplifies the technique of root-evaluation.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 51 , 1932 , pp. 80 - 90
Copyright
Copyright © Royal Society of Edinburgh 1932

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References

page 80 note * Proc. Boy. Soc. Edin., 46 (1926), pp. 289–305.

page 84 note * We reserve the word “minor” for the determinant, “submatrix” for the array.

page 84 note † Rados' Theorem (1891).

page 85 note * Muir, , Theory of Determinants, iii, p. 17.Google Scholar

page 86 note * This matrix has been called the “auxiliary unit-matrix” by Prof. H. W. Turnbull, to whom I am indebted for bringing its properties to my notice.

page 89 note * The determinant of such matrices has been studied. See Muir's History, iv, p. 178.