Ehrlich-Kjurkchiev方法在代数方程重根情形下的推广
Generalization of Ehrlich-Kjurkchiev method for multiple roots of algebraic equations
AI总结：
本文推广了Ehrlich-Kjurkchiev方法，用于同时求解具有已知重数的代数方程所有重根，无需高阶导数且保持四阶收敛速度，具有实际应用价值。
摘要：
本文提出了一种新方法，该方法是Ehrlich-Kjurkchiev方法的推广。此方法能够在代数方程的根被假定为重根且重数已知的情况下，同时求出方程的所有根。所提出的推广不需要计算高于一阶的导数，同时保持四阶收敛速度，这使得该方法从实际应用的角度来看是适用的。
英文摘要：
In this paper a new method which is a generalization of the Ehrlich-Kjurkchiev method is developed. The method allows to find simultaneously all roots of the algebraic equation in the case when the roots are supposed to be multiple with known multiplicities. The offered generalization does not demand calculation of derivatives of order higher than first simultaneously keeping quaternary rate of convergence which makes this method suitable for application from the practical point of view.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
