不同初始条件类型之间关系的研究：针对同时求根方法
Relationships between different types of initial conditions for simultaneous root finding methods
AI总结：
本文研究了同时求根方法中不同初始条件类型之间的关系，提出通过局部收敛结果获得半局部收敛结果的新方法，确保迭代方法的收敛性。
摘要：
迭代方法的初始条件构造是求解非线性方程中最重要问题之一。本文获得了保证迭代方法同时求多项式所有零点收敛的不同初始条件类型之间的关系。特别地，我们证明了任何同时方法的局部收敛定理可以转换为具有可计算验证初始条件的收敛定理，具有实际重要性。因此，我们提出了一种通过局部收敛结果获得同时方法半局部收敛结果的新方法。
英文摘要：
The construction of initial conditions of an iterative method is one of the most important problems in solving nonlinear equations. In this paper, we obtain relationships between different types of initial conditions that guarantee the convergence of iterative methods for simultaneous finding all zeros of a polynomial. In particular, we show that any local convergence theorem for a simultaneous method can be converted into a convergence theorem with computationally verifiable initial conditions which is of practical importance. Thus, we propose a new approach for obtaining semilocal convergence results for simultaneous methods via local convergence results.
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。
