The convergence of the perturbed Newton method and its application for ill-conditioned problems

作者：Peris R^*; Marquina A; Candela V

来源：Applied Mathematics and Computation, 2011, 218(7): 2988-3001.

DOI：10.1016/j.amc.2011.08.019

• Iterative methods
• Nonlinear equations
• Modified Newton method
• Ill conditioning
• Local convergence
• Stability

Iterative methods, such as Newton's, behave poorly when solving ill-conditioned problems: they become slow (first order), and decrease their accuracy. In this paper we analyze deeply and widely the convergence of a modified Newton method, which we call perturbed Newton, in order to overcome the usual disadvantages Newton's one presents. The basic point of this method is the dependence of a parameter affording a degree of freedom that introduces regularization. Choices for that parameter are proposed. The theoretical analysis will be illustrated through examples.

• 出版日期2011-12-1