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The solution of algebraic equations on the EDSAC

Published online by Cambridge University Press:  24 October 2008

R. A. Brooker
R. A. Brooker
Affiliation:
University Mathematical LaboratoryCambridge*
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Abstract

This paper is an account of the methods that have been used with the EDSAC for the solution of algebraic equations. Three repetitive or iterative methods are examined: Bernoulli's method, the root-squaring method, and the Newton-Raphson method. Experience with the EDSAC has shown that, as in hand computing, quadratically convergent methods are to be preferred to those less rapidly convergent. In particular, the Newton-Raphson method has proved the most useful. Several examples are given in the appendix.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 2 , April 1952 , pp. 255 - 270
Copyright
Copyright © Cambridge Philosophical Society 1952

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References

REFERENCES

(1)Aitken, A. C.Proc. roy. Soc. Edinb. 46 (1926), 289.Google Scholar
(2)Alt, F.Math. Tab., Wash., 3 (1948), 1 and 69.Google Scholar
(3)Bodewig, E.Quart. appl. Math. 4 (1946), 177.CrossRefGoogle Scholar
(4)Bodewig, E.Quart. appl. Math. 7 (1949), 325.CrossRefGoogle Scholar
(5)Brodetsky, S. and Smeal, G.Proc. Camb. phil. Soc. 22 (1923), 83.CrossRefGoogle Scholar
(6)Brooker, R. A. and Wheeler, D. J.Math. Tab., Wash, (in the Press).Google Scholar
(7)Dimsdale, B.Quart. appl. Math. 6 (1948), 77.CrossRefGoogle Scholar
(8)Fry, T. C.Quart. appl. Math. 3 (1945), 89.CrossRefGoogle Scholar
(9)Hartree, D. R.Eureka, 10 (1948), 13.Google Scholar
(10)Lanczos, C.Bur. Stand. J. Res., Wash., 45 (1950), 255.CrossRefGoogle Scholar
(11)Milne, W. E.Numerical calculus (Princeton, 1949), p. 53.CrossRefGoogle Scholar
(12)Ostrowski, A. M.Ada math., Stockh., 72 (1940), 99.Google Scholar
(13)Temple, S.Proc. roy. Soc. A, 169 (1939), 476.Google Scholar
(14)Turnbull, H. W.Theory of equations (Edinburgh, 1939), p. 72.Google Scholar
(15)Whittaker, E. T. and Robinson, G.The calculus of observations, 3rd ed. (London, 1940), p. 84.Google Scholar
(16)Wilkes, M. V., Wheeler, D. J. and Gill, S. The preparation of programmes for an electronic digital computer, with special reference to the EDSAC and the use of a library of subroutines (Cambridge, Mass., 1951), p. 85.Google Scholar