A fourth order method for finding a simple root of univariate function
Sbibih, D. ; Abdelhafid, Serghini ; Tijini, A. ; Zidna, A.
Boletim da Sociedade Paranaense de Matemática, Tome 34 (2015), / Harvested from Portal de Periódicos da UEM
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In this paper, we describe an iterative method for approximating asimple zero $z$ of a real defined function. This method is aessentially based on the idea to extend Newton's method to be theinverse quadratic interpolation. We prove that for a sufficientlysmooth function $f$ in a neighborhood of $z$ the order of theconvergence is quartic. Using Mathematica with its high precisioncompatibility, we present some numerical examples to confirm thetheoretical results and to compare our method with the others givenin the literature.

Publié le : 2015-01-01
DOI : https://doi.org/10.5269/bspm.v34i2.24763 
@article{24763,
     title = {A fourth order method for finding a simple root of univariate function},
     journal = {Boletim da Sociedade Paranaense de Matem\'atica},
     volume = {34},
     year = {2015},
     doi = {10.5269/bspm.v34i2.24763},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/24763}
}

Sbibih, D.; Abdelhafid, Serghini; Tijini, A.; Zidna, A. A fourth order method for finding a simple root of univariate function. Boletim da Sociedade Paranaense de Matemática, Tome 34 (2015) . doi : 10.5269/bspm.v34i2.24763. http://gdmltest.u-ga.fr/item/24763/