A sinc function analogue of chebfun

Chebfun is an established software system for computing with functions of a real variable, but its capabilities for handling functions with singularities are limited. Here an analogous system is described based on sinc function expansions instead of Chebyshev series. This experiment sheds light on the strengths and weaknesses of sinc function techniques. It also serves as a review of some of the main features of sinc methods including construction, evaluation, zero�finding, optimization, integration and di�fferentiation

Chebyshev interpolation for functions with endpoint singularities via exponential and double-exponential transforms

We present five theorems concerning the asymptotic convergence rates of Chebyshev interpolation applied to functions transplanted to either a semi-infinite or an infinite interval under exponential or double-exponential transformations. This strategy is useful for approximating and computing with functions that are analytic apart from endpoint singularities. The use of Chebyshev polynomials instead of the more commonly used cardinal sinc or Fourier interpolants is important because it enables one to apply maps to semi-infinite intervals for functions which have only a single endpoint singularity. In such cases, this leads to significantly improved convergence rates

Chopping a Chebyshev series

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\ud many years of discussion and the considerations that led to this design