An Efficient Family of Root-Finding Methods with Optimal Eighth-Order Convergence. (18th October 2012)

• Record Type: Journal Article
• Authors: Sharma, Rajni; Sharma, Janak Raj
• Other Names: Risebro Nils Henrik Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2012(2012)
• Publication Date: 2012-10-18
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2012/346420
• Languages: English
• ISSNs: 1687-9562

Abstract

Abstract : We derive a family of eighth-order multipoint methods for the solution of nonlinear equations. In terms of computational cost, the family requires evaluations of only three functions and one first derivative per iteration. This implies that the efficiency index of the present methods is 1.682. Kung and Traub (1974) conjectured that multipoint iteration methods without memory based on n evaluations have optimal order 2 n - 1 . Thus, the family agrees with Kung-Traub conjecture for the case n = 4 . Computational results demonstrate that the developed methods are efficient and robust as compared with many well-known methods.