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A Family of Optimal Eighth Order Multiple Root Finders with Multivariate Weight Function

机译：具有多元权重函数的最优八阶多重根查找器族

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摘要

Finding repeated zero for a nonlinear equation f(x) = 0, f : I ⊆ R → R, has always been of much interest and attention due to it's wide applications in many fields of science and engineering. The modified Newton's method is usually applied to solve this problem. Keeping in view that very few optimal higher order convergent methods exist for multiple roots, we present a new family of optimal eighth order convergent iterative methods for multiple roots with known multiplicity involving multivariate weight function. The numerical performance of the proposed methods is analyzed extensively along with the basins of attractions. Real life models from Life Science, Engineering and Physics are considered for the sake of comparison. The numerical experiments show that our proposed methods are efficient for determining multiple roots of non-linear equations.
机译：寻找非线性方程f（x）= 0，f：I→R→R的重复零，由于它在科学和工程学的许多领域中的广泛应用，一直备受关注和关注。修改后的牛顿法通常用于解决该问题。考虑到很少有针对多个根的最优高阶收敛方法，我们提出了一个新的针对具有多重加权函数的已知多重根的最优八阶收敛迭代方法族。所提出的方法的数值性能连同吸引力盆地被广泛分析。为了进行比较，考虑了生命科学，工程学和物理学中的现实生活模型。数值实验表明，我们提出的方法对于确定非线性方程的多重根是有效的。

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