The construction of sphericalt-designs with (t+1)2 points on the unit sphereS2 in ℝ3 can be reformulated as an underdetermined system of nonlinear equations. This system is highly nonlinear and involves the evaluation of a degreet polynomial in (t+1)4 arguments. This paper reviews numerical verification methods using the Brouwer fixed point theorem and Krawczyk interval operator for solutions of the underdetermined system of nonlinear equations. Moreover, numerical verification methods for proving that a solution of the system is a sphericalt-design are discussed.

中文翻译：

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球面设计的数值验证方法

在ℝ3 中的单位球S2 上具有(t+1)2 点的球面设计的构造可以重新表述为非线性方程的欠定系统。该系统是高度非线性的，并且涉及对 (t+1)4 参数中的度多项式的评估。本文回顾了使用 Brouwer 不动点定理和 Krawczyk 区间算子求解非线性方程组欠定系统的数值验证方法。此外，讨论了证明系统的解是球面设计的数值验证方法。