Cox, M G (2022) Explicit unconditionally numerically stable solution of a class of cubic equations. In: Advanced Mathematical and Computation tools in Metrology and Testing XII (Series on Advances in Mathematics for Applied Sciences). World Scientific, pp. 1-22. ISBN 9789811242373

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Abstract

Explicit algebraic expressions are derived for the roots of a cubic equation having one real and two complex roots. As opposed to traditional methods for direct (that is, non-iterative) solution, evaluation of the expressions is unconditionally numerically stable. A floating-point error analysis of the computations is given, which shows that the computed roots have extremely small relative errors. The computations are proved to be backward stable, that is, the computed roots are exact for a closely neighbouring cubic equation. Applications and uncertainty propagation are also considered.

Item Type:	Book Chapter/Section
Keywords:	cubic equations, direct solution, floating point, error bounds, numerical analysis, numerical stability, uncertainties
Subjects:	Mathematics and Scientific Computing > Modelling
Divisions:	Data Science
Publisher:	World Scientific
Last Modified:	20 Feb 2023 10:58
URI:	http://eprintspublications.npl.co.uk/id/eprint/9657

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