Singular rules for certain non-linear algorithms
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Certain simple non-linear algorithms which have useful application in numerical analysis have recently been introduced. When using the formulae of these algorithms it may sometimes occur that a quantity is numerically ill-determined. As a result of this and because of the way in which the algorithmic formulae are used, all quantities lying in a certain sector become ill-determined. By considering theε-,ϱ-, andq —d-algorithms in detail it is shown how this misfortune may be overcome. ALGOL programmes are developed to show how the derived formulae may be mechanized.
KeywordsComputational Mathematic Algorithmic Formula ALGOL Programme Singular Rule
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