chebfun

[Robert Boš]

How can I obtain a Chebyshev function for points in 2D space that are not uniformly distributed along the independent axis? For example, the data are described with two vectors: the first vector contains values on the independent axis (x), and the second vector contains values on the dependent axis (y).

[Kevin Silmore]

Hi Robert,

Long-time casual chebfun user here. You could always use the interp1 function (and you have a variety of different interpolants from which to choose), but do note that importantly, chebfun (and interpolant properties in general) benefits significantly in general from sampling functions at specific grid points (the roots of Chebyshev polynomials or equispaced points, in which case some special Floater-Hormann interpolants are used).

From the scientific standpoint, it's also worth asking: is your data noisy? If so, it's worth thinking about whether you really want an interpolant or if you're looking for some kind of optimization-based smoothing function. Chebfun can handle basic smoothing under known sampling errors on Chebyshev grids but not with interp1 to my knowledge (and I'm not sure how it would necessarily). Curious if others can shed more light on using chebfun in the presence of sampling errors that I don't know about!

- Kevin Silmore

On Wed, Mar 13, 2024, 3:52 AM Robert Boš <chetg...@gmail.com> wrote:

How can I obtain a Chebyshev function for points in 2D space that are not uniformly distributed along the independent axis? For example, the data are described with two vectors: the first vector contains values on the independent axis (x), and the second vector contains values on the dependent axis (y).

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