✦ LIBER ✦

Some variants of Cauchy's method with accelerated fourth-order convergence

✍ Scribed by Jisheng Kou

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 149 KB
Volume: 213
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.01.031

No coin nor oath required. For personal study only.

✦ Synopsis

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 Cauchy's method.

📜 SIMILAR VOLUMES

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 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 Newton's method with accele

A variant of Newton's method with accelerated third-order convergence

✍ S. Weerakoon; T.G.I. Fernando 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 421 KB

Some modifications of Newton's method wi

Some modifications of Newton's method with fifth-order convergence

✍ Jisheng Kou; Yitian Li; Xiuhua Wang 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 133 KB

In this paper, we present some new modifications of Newton's method for solving non-linear equations. Analysis of convergence shows that these methods have order of convergence five. Numerical tests verifying the theory are given and based on these methods, a class of new multistep iterations is dev

On convergence and performance of iterat

On convergence and performance of iterative methods with fourth-order compact schemes

✍ Jun Zhang 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 508 KB

We study the convergence and performance of iterative methods with the fourth-order compact discretization schemes for the one-and two-dimensional convection-diffusion equations. For the one-dimensional problem, we investigate the symmetrizability of the coefficient matrix and derive an analytical f

Some modifications of Newton’s method wi

Some modifications of Newton’s method with higher-order convergence for solving nonlinear equations

✍ Liang Fang; Guoping He 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 462 KB

step iterative method Order of convergence a b s t r a c t In [YoonMee Ham etal., Some higher-order modifications of Newton's method for solving nonlinear equations, J. Comput. Appl. Math., 222 (2008) 477-486], some higher-order modifications of Newton's method for solving nonlinear equations are c