Chopping a Chebyshev Series
Chopping a Chebyshev Series
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DOI：
10.1145/2998442
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发表时间：
2017-03-01
影响因子：
2.7
通讯作者：
Trefethen, Lloyd N.
中科院分区：
文献类型：
--
作者：
Aurentz, Jared L.;Trefethen, Lloyd N.
Chebfun和相关的软件项目的数值计算的功能是基于这样的想法，在每一步的计算，一个函数f（x）定义在一个区间[a，B]是“四舍五入”到一个规定的精度，通过构建一个切比雪夫系列和切碎它在一个适当的点。设计一个具有正确属性的斩波算法被证明是一个令人惊讶的复杂和有趣的问题。经过多年的讨论，我们描述了Chebfun 5.3版在2015年引入的斩波算法以及导致这种设计的考虑因素。
Chebfun and related software projects for numerical computing with functions are based on the idea that at each step of a computation, a function f(x) defined on an interval [a, b] is "rounded" to a prescribed precision by constructing a Chebyshev series and chopping it at an appropriate point. Designing a chopping algorithm with the right properties proves to be a surprisingly complex and interesting problem. We describe the chopping algorithm introduced in Chebfun Version 5.3 in 2015 after many years of discussion and the considerations that led to this design.