On Two Higher Order Enclosing Methods of J. W. Schmidt | Zendy

Alefeld G. | Zendy; Potra F. A. | Zendy

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On Two Higher Order Enclosing Methods of J. W. Schmidt

Author(s) -

Alefeld G.,

Potra F. A.

Publication year - 1988

Publication title -

zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 51

eISSN - 1521-4001

pISSN - 0044-2267

DOI - 10.1002/zamm.19880680802

Subject(s) - monotone polygon , mathematics , convergence (economics) , scalar (mathematics) , order (exchange) , function (biology) , derivative (finance) , iterative method , nonlinear system , mathematical analysis , mathematical optimization , geometry , physics , finance , quantum mechanics , evolutionary biology , financial economics , economics , biology , economic growth

We consider modifications of two iterative procedures of J. W. Schmidt which, under appropriate conditions provide monotone enclosures for the solution of a nonlinear equation. The order of convergence of the first method is 3 and in the scalar case it requires two function‐ and one derivative‐evaluation per iteration step, while the second one has the convergence order equal to 1 + √2 and it requires only two function‐evaluations per step.

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