Bivariate spline interpolation at grid points
Bivariate spline interpolation at grid points
复制标题
网格点处的双变量样条插值
DOI：
10.1007/s002110050137
复制
发表时间：
1995
影响因子：
2.1
通讯作者：
Th. Riessinger
中科院分区：
文献类型：
--
作者：
G. Nürnberger;Th. Riessinger
概括。
我们描述了用于构建点集的算法
任意程度和平滑度的双变量花纹空间为
可能的。花键是在矩形分区上定义的
每个矩形的一个或两个对角线。插值集
以分区的网格点的方式选择
这些集合包含在这些集合中，不需要求解大型线性系统。
我们的方法是生成线段的网，并选择点集
这些细分市场满足Schoenberg-Whitney条件的
某些单变量样条空间，以便一定程度的原则
可以使用还原。为了在
插值集，我们提供了足够的Schoenberg-Whitney类型
通过在某些锥体支持的双变量花键插值的条件。
这种方法完全不同
从已知的双变量插值方法中最多。
三。一些数值示例说明了我们的方法。
Summary.
We describe algorithms for constructing point sets at which interpolation by
spaces of bivariate splines of arbitrary degree and smoothness is
possible. The splines are defined on rectangular partitions adding
one or two diagonals to each rectangle. The interpolation sets
are selected in such a way that the grid points of the partition
are contained in these sets, and no large linear systems have to be solved.
Our method is to generate a net of line segments and to choose point sets in
these segments which satisfy the Schoenberg-Whitney condition for
certain univariate spline spaces such that a principle of degree
reduction can be applied. In order to include the grid points in the
interpolation sets, we give a sufficient Schoenberg-Whitney type
condition for interpolation by bivariate splines supported in certain cones.
This approach is completely different
from the known interpolation methods for bivariate splines of degree at most
three. Our method is illustrated by some numerical examples.