含区间参数非线性方程的多步区间迭代算法
Multi-Step Interval Iteration Algorithm for Nonlinear Equations with Interval Parameters
摘要: 本文在Nikas的含区间参数非线性方程的拓展区间牛顿法的基础上，结合多步区间迭代，提出了求解含区间参数非线性方程的一个拓展的多步区间迭代算法，证明新算法至少具有三阶收敛的性质，同时给出了12个数值算例，算例结果验证了新提出的多步区间迭代算法相比Nikas提出的拓展区间牛顿法在计算效率上有所提高，是有效和可靠的。
Abstract:
Based on Nikas’ extended interval Newton method for nonlinear equations with interval parameters, combined with multi-step interval iteration, this paper proposes an extended multi-step interval iteration algorithm for solving nonlinear equations with interval parameters. It proves that the new algorithm has at least three order convergence, and 12 numerical examples are given at the same time. Numerical results verify that new proposed multi-step interval iteration algorithm is effective and reliable compared with the extended interval Newton method proposed by Nikas.
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