In a recent paper almost sure unisolvence of RBF interpolation at random points with no polynomial addition was proved, for Thin-Plate Splines and Radial Powers with noninteger exponent. The proving technique left unsolved the case of odd exponents. In this short note we prove almost sure polynomial-free unisolvence in such instances, by a deeper analysis of the interpolation matrix determinant and fundamental properties of analytic functions.

翻译：在最近的一篇论文中，对于非整数指数的薄板样条和径向幂函数，证明了随机点处无多项式附加项的径向基函数插值几乎必然具有唯一可解性。该证明技术未能解决奇次指数情形。本文通过深入分析插值矩阵行列式以及解析函数的基本性质，证明了此类情形下几乎必然的多项式自由唯一可解性。