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How to increase convergence order of the Newton method to 2 × m ?

Sanjay Kumar Khattri (2014)

Applications of Mathematics

We present a simple and effective scheme for forming iterative methods of various convergence orders. In this scheme, methods of various convergence orders, such as four, six, eight and ten, are formed through a modest modification of the classical Newton method. Since the scheme considered is a simple modification of the Newton method, it can be easily implemented in existing software packages, which is also suggested by the presented pseudocodes. Finally some problems are solved, to very high...

Interval solutions of linear interval equations

Jiří Rohn (1990)

Aplikace matematiky

It is shown that if the concept of an interval solution to a system of linear interval equations given by Ratschek and Sauer is slightly modified, then only two nonlinear equations are to be solved to find a modified interval solution or to verify that no such solution exists.

New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations

Somayeh Sharifi, Massimiliano Ferrara, Mehdi Salimi, Stefan Siegmund (2016)

Open Mathematics

In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari’s method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. These class of methods have the efficiency index equal to [...] 814≈1.682 8 1 4 ≈ 1 . 682 . We describe the analysis of the proposed methods along with numerical experiments including comparison...

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