论文标题
多度B-Splines的Tchebycheffian扩展：算法计算和属性
A Tchebycheffian extension of multi-degree B-splines: Algorithmic computation and properties
论文作者
论文摘要
在本文中，我们提出了一种有效，可靠的方法，用于计算带有从扩展TchebyCheff空间的碎片的样条空间的标准化B型式的基础。扩展的Tchebycheff空间及其尺寸可以从间隔变为间隔。该方法是通过构建矩阵来绘制普通化的伯恩斯坦样基础来为b-spline感兴趣的基础来起作用的。 B-Spline样基础与经典的单变量B-Splines共享许多表征属性，并且可以很容易地将其纳入现有的样条码中。这可能有助于对Tchebycheffian在应用中的全面利用，从而使它们摆脱了多项式花纹的优雅理论扩展的受限作用。提供了数字示例，以说明所述过程。
In this paper we present an efficient and robust approach to compute a normalized B-spline-like basis for spline spaces with pieces drawn from extended Tchebycheff spaces. The extended Tchebycheff spaces and their dimensions are allowed to change from interval to interval. The approach works by constructing a matrix that maps a generalized Bernstein-like basis to the B-spline-like basis of interest. The B-spline-like basis shares many characterizing properties with classical univariate B-splines and may easily be incorporated in existing spline codes. This may contribute to the full exploitation of Tchebycheffian splines in applications, freeing them from the restricted role of an elegant theoretical extension of polynomial splines. Numerical examples are provided that illustrate the procedure described.
