Numerical differentiation by high order interpolation
Numerical differentiation by high order interpolation
复制标题
DOI：
10.1137/0908079
复制
发表时间：
1987-11
期刊：
影响因子：
--
通讯作者：
P. Hoffman;K. Reddy
中科院分区：
文献类型：
--
作者：
P. Hoffman;K. Reddy
高阶插值作为数值逼近和微分的方法进行了研究。证明了近似算子在统一范数内有界。为了减少均匀间隔点的界限，引入了涉及这些点的子集的技术。选择子集来近似切比雪夫分布。提供了数值验证以及通过伪谱方法求解偏微分方程的应用。特别关注机器精度的作用。
High order interpolation is examined as a method for numerical approximation and differentiation. The approximation operators are proved to be bounded in the uniform norm. To reduce this bound for uniformly spaced points, a technique involving subsets of these points is introduced. The subsets are chosen to approximate the Chebyshev distribution. Numerical verification and an application to the solution of partial differential equations by pseudospectral methods are provided. Particular attention is given to the role of machine precision.