The Effect of Rounding Errors on Newton-like Methods
- 1 January 1983
- journal article
- Published by Oxford University Press (OUP) in IMA Journal of Numerical Analysis
- Vol. 3 (1) , 109-118
- https://doi.org/10.1093/imanum/3.1.109
Abstract
In the presence of rounding errors the sequence of iterates generated by a Newton-like method implemented on a computer differs from the generated sequence produced in theory. We give conditions for the convergence of the generated sequence to an isolated solution of the equation F(x) = 0 and show that these conditions are violated in a neighbourhood of the solution. The relative accuracy to which one can expect to estimate the solution is shown to depend largely on the accuracy to which the mapping F is evaluated.Keywords
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