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http://dx.doi.org/10.14403/jcms.2015.28.3.491

ON CONSTRUCTING A HIGHER-ORDER EXTENSION OF DOUBLE NEWTON'S METHOD USING A SIMPLE BIVARIATE POLYNOMIAL WEIGHT FUNCTION

LEE, SEON YEONG (Department of Mathematics Dankook University)
KIM, YOUNG IK (Department of Mathematics Dankook University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.28, no.3, 2015 , pp. 491-497 More about this Journal

Abstract

In this paper, we have suggested an extended double Newton's method with sixth-order convergence by considering a control parameter ${\gamma}$ and a weight function H(s, u). We have determined forms of ${\gamma}$ and H(s, u) in order to induce the greatest order of convergence and established the main theorem utilizing related properties. The developed theory is ensured by numerical experiments with high-precision computation for a number of test functions.

Keywords

sixth-order convergence; efficiency index; bivariate weight function; asymptotic error constant;

Citations & Related Records

Reference

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