Efficient Use of Newton's Method

摘要

Theorems of L. V. Kantorovich are used to compare the overall efficiency of Newton's method and its modified form for the approximate solution of systems of equations. Criteria are given for choosing the method to achieve given accuracy in minimum time. This comparison and decision process may be incorporated directly into computer programs, and the basic analysis involved applies to any iterative process for which the convergence rate is known. (Author)