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- Title
Extending the Applicability of Two-Step Solvers for Solving Equations.
- Authors
Argyros, Ioannis K.; Shakhno, Stepan
- Abstract
We present a local convergence of two-step solvers for solving nonlinear operator equations under the generalized Lipschitz conditions for the first- and second-order derivatives and for the first order divided differences. In contrast to earlier works, we use our new idea of center average Lipschitz conditions, through which, we define a subset of the original domain that also contains the iterates. Then, the remaining average Lipschitz conditions are at least as tight as the corresponding ones in earlier works. This way, we obtain weaker sufficient convergence criteria, larger radius of convergence, tighter error estimates, and better information on the solution. These extensions require the same effort, since the new Lipschitz functions are special cases of the ones in earlier works. Finally, we give a numerical example that confirms the theoretical results, and compares favorably to the results from previous works.
- Subjects
STOCHASTIC convergence; NONLINEAR operator equations; LIPSCHITZ spaces; GROUP extensions (Mathematics); MATHEMATICAL functions; ITERATIVE methods (Mathematics)
- Publication
Mathematics (2227-7390), 2019, Vol 7, Issue 1, p62
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math7010062