论文标题
部分可观测时空混沌系统的无模型预测
Sobolev-Orthogonal Systems with Tridiagonal Skew-Hermitian Differentiation Matrices
论文作者
论文摘要
我们介绍并开发了关于Sobolev内部产品在真实线上的正交性理论，该产品具有三角形，偏斜的分化矩阵的函数序列。尽管已经建立了这种L2-正交系统的理论，但Sobolev正交性需要新的概念及其分析。我们将这种系统完全表征为正交多项式的适当称重的傅立叶变换，并提供了许多说明性示例，其中包括一个sobolev-ottrodonal系统，其领先的N系数可以在$ \ Mathcal {o}（O}（O}（n \ log log n）$操作中计算。
We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences of functions with a tridiagonal, skew-Hermitian differentiation matrix. While a theory of such L2-orthogonal systems is well established, Sobolev orthogonality requires new concepts and their analysis. We characterise such systems completely as appropriately weighed Fourier transforms of orthogonal polynomials and present a number of illustrative examples, inclusive of a Sobolev-orthogonal system whose leading N coefficients can be computed in $\mathcal{O}(N \log N)$ operations.
