A fourth order method for finding a simple root of univariate function
In this paper, we describe an iterative method for approximating a simple zero $z$ of a real defined function. This method is a essentially based on the idea to extend Newton's method to be the inverse quadratic interpolation. We prove that for a sufficiently smooth function $f$ in a neighborho...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática
2016-08-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/24763 |
| Summary: | In this paper, we describe an iterative method for approximating a
simple zero $z$ of a real defined function. This method is a
essentially based on the idea to extend Newton's method to be the
inverse quadratic interpolation. We prove that for a sufficiently
smooth function $f$ in a neighborhood of $z$ the order of the
convergence is quartic. Using Mathematica with its high precision
compatibility, we present some numerical examples to confirm the
theoretical results and to compare our method with the others given
in the literature. |
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| ISSN: | 0037-8712 2175-1188 |