Schröder-like algorithms for multiple complex zeros of a polynomial |
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Authors: | Prof. Dr. M. S. Petković |
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Affiliation: | 1. Faculty of Electronic Engineering, Beogradska 14, P. O. Box 73, YU-18000, Ni?, Yugoslavia
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Abstract: | Using the iterative method of Newton's type in circular arithmetic, introduced in [14], a new iterative method for finding a multiple complex zero of a polynomial is derived. This method can be regarded as a version of classical Schröder's method. Initial conditions which guarantee a safe convergence of the proposed method are stated. The increase of the computational efficiency is achieved by a combination of the complex approximation methods of Schröder's type with some interval methods. The presented algorithms are analysed in view of their efficiency and illustrated numerically in the example of a polynomial equation. |
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