On the convergence condition of generalized root iterations for the inclusion of polynomial zeros

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• 作者：Miodrag S. Petkovi&#x107 ; Duš ; an M. Miloš ; evi&#x107
• 关键词：Polynomial zeros ; Simultaneous methods ; Inclusion methods ; Convergence conditions ; Circular interval arithmetic
• 刊名：Mathematics and Computers in Simulation
• 出版年：2008
• 期刊代码：88_03784754
• 类别：cp
• 出版时间：June 2008
• 卷：78
• 期：1
• 页码：12-26
• 文件大小：243 K

摘要

Using a fixed point relation based on the logarithmic derivative of the k-th order of an algebraic polynomial and the definition of the k-th root of a disk, a family of interval methods for the simultaneous inclusion of complex zeros in circular complex arithmetic was established by Petković [M.S. Petković, On a generalization of the root iterations for polynomial complex zeros in circular interval arithmetic, Computing 27 (1981) 37–55]. In this paper we give computationally verifiable initial conditions that guarantee the convergence of this parallel family of inclusion methods. These conditions are significantly relaxed compared to the previously stated initial conditions presented in literature.