Geodesic
A~modified quadratic interpolation method for~root finding
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 3, pp. 5-13

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Mots-clés : quadratic interpolation
Keywords: modeling, efficiency function of a hydraulic turbine, spline, multidimensional approximation. 
@article{SJIM_2023_26_3_a0,
     author = {V. V. Bogdanov and Yu. S. Volkov},
     title = {A~modified quadratic interpolation method for~root finding},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {5--13},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2023_26_3_a0/}
}
TY  - JOUR
AU  - V. V. Bogdanov
AU  - Yu. S. Volkov
TI  - A~modified quadratic interpolation method for~root finding
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2023
SP  - 5
EP  - 13
VL  - 26
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2023_26_3_a0/
LA  - ru
ID  - SJIM_2023_26_3_a0
ER  - 
%0 Journal Article
%A V. V. Bogdanov
%A Yu. S. Volkov
%T A~modified quadratic interpolation method for~root finding
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2023
%P 5-13
%V 26
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2023_26_3_a0/
%G ru
%F SJIM_2023_26_3_a0
V. V. Bogdanov; Yu. S. Volkov. A~modified quadratic interpolation method for~root finding. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 3, pp. 5-13. http://geodesic.mathdoc.fr/item/SJIM_2023_26_3_a0/