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This package provides multi-dimensional h-adaptive Chebyshev interpolation with the
routine hchebinterp. The routine uses a Chebyshev
basis to construct a
piecewise polynomial interpolant of an arbitrary smooth function. It depends on
FastChebInterp.jl and is
inspired by Chebfun.
To construct a polynomial interpolant p of the function f on the interval
[a,b] to a user-specified tolerance can be done with the interface
using HChebInterp
f(x) = sin(exp(x^2))
p = hchebinterp(f, 0, 1; atol=1e-5)Then p can be evaluated using its functor interface at any point in the
interpolation interval, e.g p(0.5).
The same routine also supports interpolation of multidimensional functions,
though note that the function must accept SVector inputs.
For example, a 2d function can be interpolated as follows:
g(x) = cis(prod(x))
p = hchebinterp(g, (0,0), (1,1); atol=1e-5)with evaluation at points in the support of the interpolant like p([0.1, 0.4]).
The package can interpolate any numeric or array-valued types. It also supports a batching interface. See the documentation linked above for details.
The algorithm of hchebinterp is based on the one described by Kaye et
al., (2023)
HChebInterp.jl was written by Lorenzo Van Muñoz, and is free/open-source software under the MIT license.