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Modification of iterative processes for improved convergence characteristics
Author(s) -
Lawther R.
Publication year - 1980
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620150804
Subject(s) - convergence (economics) , sequence (biology) , iterative method , iterative and incremental development , local convergence , rate of convergence , process (computing) , nonlinear system , mathematical optimization , mathematics , computer science , algorithm , key (lock) , genetics , software engineering , computer security , physics , quantum mechanics , economics , biology , economic growth , operating system
A method for improving the convergence rate of iterative processes is presented. This method monitors the sequence of approximations produced by an iterative process, and generates a new iterative process, or sequence of processes, each with more rapid convergence characteristics than the previous one. This method of process modification can be applied to many iterative techniques currently in use. Examples of application of the method are given, using both nonlinear and linear systems. In one of these examples it is shown that the method can be applied to a divergent iterative process, producing a convergent one. It is also shown how the technique can be applied to equations of one variable, yielding a method with convergence characteristics similar to those of Newton's method, but without the explicit calculation of derivatives.