Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4636757 | Applied Mathematics and Computation | 2006 | 6 Pages |
Abstract
By extending the classical Newton's irrational method defined by an iterationxn+1=xn-f(xn)fâ²(xn)2-f(xn)fâ³(xn),we present a high-order k-fold pseudo-Newton's irrational method for locating a simple zero of a nonlinear equation. Its order of convergence is proven to be at least k + 3 and the convergence behavior of the asymptotic error constant is investigated near the corresponding simple zero. A root-finding algorithm is described as well as the introduction on the convergence of the fixed-point iterative method. Various numerical examples have successfully demonstrated a good agreement with the theory presented here.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Young Hee Geum, Young Ik Kim, Min Surp Rhee,