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- Title
Iterative method for solving nonlinear singular problems.
- Authors
Prusińska, Agnieszka; Tret'yakov, Alexey
- Abstract
The aim of our work is to present a method ( p-factor method) for solving nonlinear equations of the form in singular (irregular) case, i.e. when the matrix $$F'(x)$$ is singular at an initial point $$x_0$$ of an iterative sequence $$\{x_k\}$$ , $$k=1,2,\ldots $$ We investigate conditions that have to be fulfilled at the initial point $$x_0$$ to obtain the existence of solution of nonlinear equation $$F(x)=0$$ , prove convergence of the presented p-factor method and give estimation of convergence rate for this method.
- Subjects
ITERATIVE methods (Mathematics); NUMERICAL analysis; NONLINEAR equations; STOCHASTIC convergence; MATRICES (Mathematics)
- Publication
Calcolo, 2016, Vol 53, Issue 4, p635
- ISSN
0008-0624
- Publication type
Article
- DOI
10.1007/s10092-015-0166-8