𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A new family of modified Ostrowski’s methods with accelerated eighth order convergence

✍ Scribed by Janak Raj Sharma; Rajni Sharma

Publisher
Springer US
Year
2009
Tongue
English
Weight
298 KB
Volume
54
Category
Article
ISSN
1017-1398

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

A family of modified Ostrowski’s methods
A family of modified Ostrowski’s methods with optimal eighth order of convergence
✍ Alicia Cordero; Juan R. Torregrosa; María P. Vassileva 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 214 KB

In this paper, we derive a new family of eighth-order methods for obtaining simple roots of nonlinear equations by using the weight function method. Each iteration of these methods requires three evaluations of the function and one evaluation of its first derivative, so that their efficiency indices

Some variants of Ostrowski's method with
Some variants of Ostrowski's method with seventh-order convergence
✍ Jisheng Kou; Yitian Li; Xiuhua Wang 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 135 KB

In this paper, we present a class of new variants of Ostrowski's method with order of convergence seven. Per iteration the new methods require three evaluations of the function and one evaluation of its first derivative and therefore this class of methods has the efficiency index equal to 1.627. Num

A variant of Cauchy's method with accele
A variant of Cauchy's method with accelerated fifth-order convergence
✍ M Grau; M Noguera 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 440 KB

We suggest an improvement to the iteration of Cauchy's method viewed as a generalization of possible improvements to Newton's method. Two equivalent derivations of Cauchy's method are presented involving similar techniques to ones that have been proved successfully for Newton's method. First, an ada

Some variants of Cauchy's method with ac
Some variants of Cauchy's method with accelerated fourth-order convergence
✍ Jisheng Kou 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 149 KB

In this paper, we present some variants of Cauchy's method for solving non-linear equations. Analysis of convergence shows that the methods have fourth-order convergence. Per iteration the new methods cost almost the same as Cauchy's method. Numerical results show that the methods can compete with C

New modifications of Potra–Pták’s method
New modifications of Potra–Pták’s method with optimal fourth and eighth orders of convergence
✍ Alicia Cordero; José L. Hueso; Eulalia Martínez; Juan R. Torregrosa 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 288 KB

## a b s t r a c t In this paper, we present two new iterative methods for solving nonlinear equations by using suitable Taylor and divided difference approximations. Both methods are obtained by modifying Potra-Pták's method trying to get optimal order. We prove that the new methods reach orders