A~modified quadratic interpolation method for~root finding

V. V. Bogdanov ; Yu. S. Volkov

Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 3, pp. 5-13.

Résumé

A modification of the quadratic interpolation method for finding the root of a continuous function is proposed. Two quadratic interpolation polynomials are simultaneously constructed. It is shown that if the third derivative of the original function does not change sign on the considered interval of localization of the required root, then the root lies between the roots of the quadratic functions. This allows to significantly narrow the localization interval and reduce the number of steps to calculate the root with a given accuracy. The proposed modification of the quadratic interpolation method is used in the problem of calculating isolines when modeling the hill diagram of hydraulic turbines.

Détail

Mots-clés : quadratic interpolation
Keywords: modeling, efficiency function of a hydraulic turbine, spline, multidimensional approximation.

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