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A new class of interval methods with higher order of convergence
Authors:G. Alefeld  F. Potra
Affiliation:1. Institut für Angewandte Mathematik, Universit?t Karlsruhe, Kaiserstrasse 12, D-7500, Karlsruhe, Federal Republic of Germany
2. Department of Mathematics, University of Iowa, 117 522 42, Iowa City, U.S.A.
Abstract:In this paper we introduce a new class of interval methods for enclosing a simple root of a nonlinear equation. For each nonnegative integerp we describe an iterative procedure belonging to this class which requiresp+1 function values and an interval evaluation of the second derivative per step. The order of convergence of the iterative procedure grows exponentially withp. Forp≥4 this order is strictly greater than (left( {frac{{1 + sqrt 5 }}{2}} right)^{p + 2} ) .
Keywords:
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