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Gauss-Newton method for convex optimization
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
The goal in this chapter is to present a finer convergence analysis of Gauss–Newton method than in earlier works in order to expand the solvability of convex composite optimizations problems. The convergence of Gauss–Newton ...
Osada method
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter the applicability of the Osada method for solving nonlinear equations is extended. Moreover, some examples are also presented illuminating the theoretical results.
Toward a general theory of point to point iterative processes free of derivatives with quadratic convergence
(AIP Conference Proceedings, 2018)
In this work, we are concerned with the problem of developing a general theory about derivative-free iterative procedures with quadratic convergence. Newton's method is the most used, well-known and studied in order to ...
On a Newton-type family of high-order iterative methods for some matrix functions
(AIP Conference Proceedings, 2018)
The main goal of this paper is to approximate some matrix functions by using a family of high-order Newton-type iterative methods. We analyse the semilocal convergence and the speed of convergence of these methods. Concerning ...
Secant-like methods in chemistry
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we provide different semilocal and local results for the convergence of secant-like methods in order to expand the solvability of nonlinear equations. Different numerical examples and chemical applications ...
Generalized equations
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we present some developments for the local convergence of Newton's method. Some special cases and a numerical example illuminating the theoretical results are also presented.
Laguerre-like method for multiple zeros
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter the applicability of the Laguerre-like method for finding multiple zeros is extended. Numerical examples are also presented.
Robust convergence of Newton's method for cone inclusion problem
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter, motivated by the idea of the restricted convergence domains, we present a convergence analysis of Newton's method for cone inclusion problems. The semilocal convergence analysis of Newton's method is also ...
Newton's method to solve equations with solutions of multiplicity greater than one
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter the solvability of equations with multiple roots is expanded using the modified Newton's method. Examples are also presented illuminating the theoretical results.
Convergence planes of iterative methods
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter we study the convergence planes associated to a certain class of iterative methods.