Durand-Kerner型同时包含法的最优收敛条件

2006 Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing Pub Date : 2006-09-26 DOI:10.1109/SYNASC.2006.74

Octavian Cira, Cristian Cira

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引用次数: 1

摘要

为了求解复数多项式只有简单零的代数方程，可以使用同时包含法。采用点估计理论的Durand-Kerner同时包含法的二次收敛条件为w(0) < d(0)/(an+b)，其中n为多项式次，d(0)为初始迭代与w(0)之间的最小距离为weerstrass因子的绝对最大值。本文确定了广义Durand-Kerner型同时包含法的最优二次收敛条件

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The Optimum Convergence Condition for the Durand-Kerner Type Simultaneous Inclusion Method

In order to solve the algebraic equation, where the complex polynomial has only simple zeros, one can use the simultaneous inclusion methods. The quadratic convergence condition for the Durand-Kerner simultaneous inclusion method, using point estimation theory is w(0) < d(0)/(an+b), where n is the polynomial degree, d(0) the minimum distance between the initial iterations and w(0) is the absolute maximum of the Weierstrass factors. This paper determines the optimum quadratic convergence condition for a generalized Durand-Kerner type simultaneous inclusion method

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2006 Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing

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