6533b860fe1ef96bd12c37aa
RESEARCH PRODUCT
The convergence of the perturbed Newton method and its application for ill-conditioned problems
Rosa M. PerisAntonio MarquinaVicente F. Candelasubject
Mathematical optimizationIterative methodApplied MathematicsSteffensen's methodNewton's method in optimizationLocal convergenceComputational Mathematicssymbols.namesakeNonlinear systemNewton fractalSecant methodsymbolsNewton's methodMathematicsdescription
Abstract 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-12-01 | Applied Mathematics and Computation |