Extended Local Convergence of Newton's Algorithm for Solving Strongly Regular Generalized Equations

摘要

The convergence region in the study of most algorithms for solving equations is not large and the error estimates are pessimistic in general.We develop a technique which enlarges the convergence region, tightens the error estimates and gives a more precise location for the solution without additional conditions.The technique is appled on Newton's algorithm and extends its applicability.However, it is so general that it can be applied on other algorithms with the same advantages.A numerical example is used to illustrate the new advantages.