A sequential implicit function theorem for the chords iteration

In this paper we study the local convergence of the method in order to find the solution of the generalized equation We first show that under the strong metric regularity of the linearization of the associated mapping and some additional assumptions regarding dependence on the parameter and the rela...

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Bibliographic Details
Published in:Mathematica Slovaca Vol. 63; no. 5; pp. 1085 - 1100
Main Author: Nedelcheva, Diana Kirilova
Format: Journal Article
Language:English
Published: Vienna Springer Vienna 01.10.2013
Versita
Subjects:
Algebra
chords method
generalized equations
implicit function theorem
linear convergence
Mathematics
Mathematics and Statistics
Newton-type method
Primary 49M15, 49J53
Regular Paper
Secondary 65J15, 90C31, 47H04, 65K10
set-valued mapping
strong regularity
variational inequalities
generalized equations
Primary 49M15, 49J53
Newton-type method
linear convergence
set-valued mapping
strong regularity
variational inequalities
chords method
Secondary 65J15, 90C31, 47H04, 65K10
implicit function theorem
ISSN:0139-9918, 1337-2211
Online Access:Get full text
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Summary:In this paper we study the local convergence of the method in order to find the solution of the generalized equation We first show that under the strong metric regularity of the linearization of the associated mapping and some additional assumptions regarding dependence on the parameter and the relation between the operator A and the Jacobian , we prove linear convergence of the method which is uniform in the parameter p . Then we go a step further and obtain a sequential implicit function theorem describing the dependence of the set of sequences of iterates of the parameter.
ISSN:0139-9918
1337-2211
DOI:10.2478/s12175-013-0157-7