Extended Schröder’s method and the  two quadratic convergence formulas

Shunji Horiguchi

doi:10.51094/jxiv.2544

##article.authors##

Shunji Horiguchi Independent Researcher

DOI:

https://doi.org/10.51094/jxiv.2544

キーワード:

Schröder’s method、 Newton's method

抄録

We give an extended Schröder’s method from extended Newton’s method. We then derive two quadratic convergence formulas from the extended Schröder’s method. Next, the condition under which the extended Schröder’s method is equal to or faster than the Schröder's method in converging to the m-multiple root of f(x)=0 is given. Finally, we give examples.

利益相反に関する開示

The authors declare no conflicts of interest.

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引用文献

S. Horiguchi, The Formulas to Compare the Convergences of Newton’s Method and the Extended Newton’s Method(Tsuchikura-Horiguchi’s Method) and the Numerical Calculations, Applied Mathematics

http://dx.doi.org/10.4236/am.2016.71004

S. Horiguchi, Binomial expansion of Newton’s method,

http://arxiv.org/abs/2109.12362

E. Schröder, Ueber unendlich viele Algorithmen zur Auflösung der Gleichungen, Math. Annal., 2(1870), 317-365.

H. Nagasaka,『Computers and Numerical Analysis 』(In Japanese), Asakura Publishing Co., Ltd.,1980.