Given a nonconvex minimization problem where the objective function is nonlinear and twice differentiable. To gain more information about the objective function, it is essential to obtain all its stationary points and study the behaviour of these points. Since many nonlinear functions are expressible as polynomials via interpolation, there is a need to devise fast and accurate algorithms in finding root(s) of the interpolating polynomial. Through interval computation, the Weierstrass-like parallel iterative methods are known for their efficiency in finding polynomial zeros. However, these schemes are highly dependent on the midpoints of each interval in generating successive intervals. In this study, we propose a scaling function on some Weierstrass-like parallel iterative methods such that the procedures are less dependent on the generated midpoints, hence allowing a more efficient search for the zeros while reducing the width of the intervals. The proposed procedures with the shifted centres of the enclosing intervals are tested on 120 problems and we compare their efficiency with the existing Weierstrass-like methods in terms of the number of iterations and largest final interval width. The results indicate that the proposed procedures outperform the original procedures, giving more reduction on the final interval width with a lesser number of iterations.

给定一个非凸最小化问题，其中目标函数是非线性的且可二次微分。为了获得有关目标函数的更多信息，必须获取其所有静止点并研究这些点的行为。由于许多非线性函数可以通过插值表示为多项式，因此需要设计快速准确的算法来找到插值多项式的根。通过区间计算，类似 Weierstrass 的并行迭代方法以其在找到多项式零点方面的效率而闻名。然而，这些方案在生成连续区间时高度依赖每个区间的中点。在这项研究中，我们在一些类似 Weierstrass 的并行迭代方法上提出了一个缩放函数，这样程序就较少依赖于生成的中点，因此可以更有效地搜索零点，同时减少间隔的宽度。在 120 个问题上测试了所提出的具有封闭区间中心偏移的程序，我们将它们与现有的类似 Weierstrass 的方法在迭代次数和最大最终区间宽度方面的效率进行了比较。结果表明，所提出的程序优于原始程序，以更少的迭代次数更多地减少最终间隔宽度。在 120 个问题上测试了所提出的具有封闭区间中心偏移的程序，我们将它们与现有的类似 Weierstrass 的方法在迭代次数和最大最终区间宽度方面的效率进行了比较。结果表明，所提出的程序优于原始程序，以更少的迭代次数更多地减少最终间隔宽度。在 120 个问题上测试了所提出的具有封闭区间中心偏移的程序，我们将它们与现有的类似 Weierstrass 的方法在迭代次数和最大最终区间宽度方面的效率进行了比较。结果表明，所提出的程序优于原始程序，以更少的迭代次数更多地减少最终间隔宽度。