In this paper we present an approach which predicts directly without search the optimal choice of the shape parameter c contained in the multiquadrics $(-1){}^{\lceil \frac{\beta }{2}\rceil }(c^2+{\parallel x\parallel }^2){}^{\frac{\beta }{2}},\beta >0,$ and the inverse multiquadrics $(c^2+{\parallel x\parallel }^2){}^{\frac{\beta }{2}},\beta <0$. Unlike the simplex scheme where the data points are required to be evenly spaced, as in a recent paper of the author, here we allow them to be arbitrarily scattered in the simplex, making it much more useful. Besides this, we aim at helping non-mathematicians use our approach and hence remove some complicated requirements for the domain. The drawback is that its theoretical ground is not so strong as in the evenly spaced data setting. However, experiments show that it works well. The experimentally optimal value of c coincides with the theoretically predicted one. Since the fill distance, which reflects the amount of data points needed, involved is always of reasonable size, this approach is supposed to be practically useful.

在本文中，我们提出一种无需预测即可直接预测多二次方程中包含的形状参数c的最佳选择的方法。$（-\mathrm{1个}）{}^{\lceil \frac{\beta }{2}\rceil }（C^2+{\parallel X\parallel }^2）{}^{\frac{\beta }{2}}，\beta >0，$ 和逆多二次元 $（C^2+{\parallel X\parallel }^2）{}^{\frac{\beta }{2}}，\beta <0$。不同于在作者的最新论文中要求数据点均匀分布的单纯形方案，这里我们允许将它们任意散布在单纯形中，使其更加有用。除此之外，我们旨在帮助非数学家使用我们的方法，从而消除对该领域的一些复杂要求。缺点是它的理论基础不如在均匀间隔的数据设置中那么牢固。但是，实验表明它运作良好。c的实验最优值与理论预测值一致。由于填充距离（反映所需的数据点的数量）始终具有合理的大小，因此该方法被认为是实用的。