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- Title
Semilocal Convergence of a Newton-Secant Solver for Equations with a Decomposition of Operator.
- Authors
Argyros, Ioannis K.; Shakhno, Stepan; Yarmola, Halyna
- Abstract
We provide the semilocal convergence analysis of the Newton-Secant solver with a decomposition of a nonlinear operator under classical Lipschitz conditions for the first order Fréchet derivative and divided differences. We have weakened the sufficient convergence criteria, and obtained tighter error estimates. We give numerical experiments that confirm theoretical results. The same technique without additional conditions can be used to extend the applicability of other iterative solvers using inverses of linear operators. The novelty of the paper is that the improved results are obtained using parameters which are special cases of the ones in earlier works. Therefore, no additional information is needed to establish these advantages.
- Subjects
OPERATOR equations; NEWTON-Raphson method; NONLINEAR operators; LINEAR operators; CLASSICAL conditioning; INFORMATION needs
- Publication
Journal of Computational Analysis & Applications, 2021, Vol 29, Issue 2, p279
- ISSN
1521-1398
- Publication type
Article