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Numerical Maximization of Derivatives by Successive Polynomial Interpolation
Author(s) -
Van Griend J. A. De
Publication year - 1984
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.19840640610
Subject(s) - interpolation (computer graphics) , convergence (economics) , mathematics , polynomial , maximization , class (philosophy) , variable (mathematics) , function (biology) , mathematical optimization , computer science , mathematical analysis , artificial intelligence , motion (physics) , evolutionary biology , economics , biology , economic growth
A general class of numerical methods for maximizing derivatives of a real function in one variable is presented. These methods (the so‐called SPI methods) are based on successive polynomial interpolation. Our class includes known methods of Tamir and of Brent. In this paper we derive the order of convergence of the general SPI‐methods, thus generalizing related convergence results for some special methods obtained before by Brent, Burmeister, Schmidt and Tamir.