The solution of algebraic equations on the EDSAC
- 1 April 1952
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 48 (2), 255-270
- https://doi.org/10.1017/s0305004100027614
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.Keywords
This publication has 8 references indexed in Scilit:
- An iteration method for the solution of the eigenvalue problem of linear differential and integral operatorsJournal of Research of the National Bureau of Standards, 1950
- Numerical CalculusPublished by Walter de Gruyter GmbH ,1949
- On types of convergence and on the behavior of approximations in the neighborhood of a multiple root of an equationQuarterly of Applied Mathematics, 1949
- On Bernoulli’s method for solving algebraic equationsQuarterly of Applied Mathematics, 1948
- On Graeffe’s method for solving algebraic equationsQuarterly of Applied Mathematics, 1946
- Some numerical methods for locating roots of polynomialsQuarterly of Applied Mathematics, 1945
- The general theory of relaxation methods applied to linear systemsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1939
- On Graeffe's Method for Complex Roots of Algebraic EquationsMathematical Proceedings of the Cambridge Philosophical Society, 1924