Asymptotic error constants of cubically convergent zero finding methods
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摘要
The Laguerre family of iteration functions for finding multiple zeros is considered. This family is algebraically equivalent to the multiple zero counterpart of Hansen–Patrick family. The asymptotic error constant for the Laguerre family is given. The magnitude of asymptotic error constants for cubically convergent iteration functions for finding multiple real zeros of real functions are compared. Numerical examples are given.
论文关键词：Laguerre family,Hansen–Patrick family,Ostrowski square root method,Halley method,Halley's irrational method,Euler–Chebyshev method,Asymptotic error constant,Multiple zero,One-point iteration
论文评审过程：Received 15 January 2005, Revised 24 July 2005, Available online 2 December 2005.
论文官网地址：https://doi.org/10.1016/j.cam.2005.09.016
