Alternative convergence criteria for iterative methods of solving nonlinear equations

✍ Scribed by Hamilton A. Chase

• Publisher: Elsevier Science
• Year: 1984
• Tongue: English
• Weight: 877 KB
• Volume: 317
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(84)90035-8

✦ Synopsis

x,,, -J, m = 1, 2, 3 . . be an iteration method for solving the nonlinear problem F(X) = 0, where F(X) and its derivatives possess all of the properties required by T(x,,,). Then ifit can be established thatfor the problem at hand jlF(~,+ 1)i/ < &,, llF(x& V m > M,, (M, < co) and 0 < &,, < 1, dejinitions are established and theorems proven concerning convergence, uniqueness and bounds on the error after 'm' successive iterations of a new approach to convergence properties T&J. These characteristics are referred to as "alternate" (local, global) convergence properties and none of the proofs given are restricted to any specijc type of method such as, e.g. contraction mapping types. Application of results obtained are illustrated using Newton's method as well as the general concept of Newton-like methods.