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Zotter conveniently offers a variety of additional beam weights here:
> [Ultraspherical/Gegenbauer polynomials to unify 2D/3D Ambisonic directivity designs](https://arxiv.org/abs/2401.00813)
_Th…
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I am using Krylov methods to solve a non-symmetric system arising from spectral Galerkin PDE discretization. The system converges with GMRES but it takes quite a lot of iterations. I am not that famil…
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The first computation of an integral on a 2D ultraspherical space seems to be extremely slow:
```
> using ApproxFun
> U = Ultraspherical(1, 0..1)^2;
> Q = DefiniteIntegral(U[1]) ⊗ DefiniteIn…
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I have a big `BanedBlockBandedMatrix` and need to multiply it with a vector. However it seems to be rather slow and require a lot of allocation. Here's a MWE
```
using BlockArrays: BlockRange
usi…
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In lecture16, here are several codes:
S₀ = I : Chebyshev() → Ultraspherical(1)
f = Fun(exp, Chebyshev())
g = S₀*f
g(4) - exp(4)
I found the error when I run it:
UndefVarError: I not defined
…
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When trying to use ApproxFun to interpolate a function on Chebyshev-points and compute derivatives, I came across the following behaviour:
Define two spaces of Chebyshev and ultraspherical polynomi…
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The abs() fails on a forth order derivative where is succeeds on the third order. This looks like a regression since it did work in the November timeframe (this is on ApproxFun master). Details belo…
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We currently depend on chebfun for a few tasks, namely fast transforms, ultraspherical computations, and low-rank approximation of variable PDE coefficients (which should hopefully be obviated by #4).…
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```julia
julia> x = rand(1000);
julia> y1 = @btime FastTransforms.cheb2ultra($x, 2);
24.224 ms (2 allocations: 7.98 KiB)
julia> y2 = @btime ApproxFunBase.mul_coefficients(Conversion(Chebyshe…
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In the test directory, include code function values of different polynomials as tests to verify answers are correct.
I have yet to find a more efficient method than copy pasting the [pdf archives](ht…