The Systematic Formation of High-Order Iterative Methods

Journal of Applied & Computational Mathematics

article

Isaac Fried¹ 

[1] Department of Mathematics, Boston University

关键词: Fixed point iteration;    The generation of high order iterative functions;    The Taylor-Lagrange formula;    High-order iterative methods;    Undetermined coefficients;    Contrary and alternating convergence;    Root bracketing;   

DOI  :  10.4172/2168-9679.1000165

来源: Hilaris Publisher

【 摘 要 】

Fixed point iteration and the Taylor-Lagrange formula are used to derive, some new, efficient, high-order, up to octic, methods to iteratively locate the root, simple or multiple, of a nonlinear equation. These methods are then systematically modified to account for root multiplicities greater than one. Also derived, are super-quadratic methods that converge contrarily, and super-linear and super-cubic methods that converge alteratingly, enabling us, not only to approach the root, but also to actually bound and bracket it.

【 授权许可】

Unknown