Extending the applicability of high-order iterative schemes under Kantorovich hypotheses and restricted convergence regions

Ioannis K. Argyros, Santhosh George, Shobha M. Erappa

Research output: Contribution to journalArticle

Abstract

We use restricted convergence regions to locate a more precise set than in earlier works containing the iterates of some high-order iterative schemes involving Banach space valued operators. This way the Lipschitz conditions involve tighter constants than before leading to weaker sufficient semilocal convergence criteria, tighter bounds on the error distances and an at least as precise information on the location of the solution. These improvements are obtained under the same computational effort since computing the old Lipschitz constants also requires the computation of the new constants as special cases. The same technique can be used to extend the applicability of other iterative schemes. Numerical examples further validate the new results.

Original languageEnglish
JournalRendiconti del Circolo Matematico di Palermo
DOIs
Publication statusAccepted/In press - 01-01-2019
Externally publishedYes

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High-order Schemes
Iterative Scheme
Semilocal Convergence
Convergence Criteria
Lipschitz condition
Iterate
Lipschitz
Banach space
Sufficient
Numerical Examples
Computing
Operator

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Extending the applicability of high-order iterative schemes under Kantorovich hypotheses and restricted convergence regions. / Argyros, Ioannis K.; George, Santhosh; Erappa, Shobha M.

In: Rendiconti del Circolo Matematico di Palermo, 01.01.2019.

Research output: Contribution to journalArticle

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