Stepsize selection in continuation procedures and damped Newton's method

摘要

In this work we explore the relation of the problem of satisfying a sufficient decrease criterion in a damped Newton's method to the problem of stepsize selection for continuation methods. We show that there is a strong connection between the two, and that standard line search techniques used for computing damping parameters have direct application to the stepsize selection problem. The performance of the resulting continuation technique is demonstrated for several standard example problems.