# Questions tagged [chebyshev]

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9 questions
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### Numerical analysis: Chebyshev coefficient representation error

If $x_k$ are the Chebyshev nodes, that is for $n \in \mathbb{N}^*$, we have $x_k = \cos(\pi \frac{2k + 1}{n})$. Now suppose you have approximated values of $x_k$ and $x_{k'}$ for $k,k' \leq n$. In the ...
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### Padua-type pointset for functions singular on line $x=y$

The Padua points $\mathrm{Pad}_{n} \subset [-1,1]^{2}$ are a unisolvent pointset with optimal growth of Lebesgue constant, described in detail here. With some work they can be used to generate a ...
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### What is Chebfun eigs doing

What is this doing? Looks like the original eigenvalue problem is converted into generalized eigenvalue problems with different dimensions of collocation points. Can someone explain more about this? ...
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I was looking for some help with derivatives of Chebychev polynomials at zero points. The recursive expression, $$T_{(j+1)}(x) = 2xT_j(x) - T_{(j-1)}(x)$$ has the derivative T'_{j+1}(x) = 2T_j(... 0answers 35 views ### Extracting Real Part of Twiddle Factors from fftw_plan When calculating a type-II DCT with FFTW, you create an fftw_plan, via ... 1answer 166 views ### Clenshaw-type recurrence for derivative of Chebyshev series The naive summation of a Chebyshev series \begin{align*} f(x) = \frac{c_0}{2} + \sum_{k=1}^{n-1} c_{k}T_{k}(x) \end{align*} which employs the three-term recurrence for evaluation of the Chebyshev ... 0answers 62 views ### Solve a PDE BVP with Spectral methods in time and space? I have a PDE (coming from a Bellman equation with z under brownian motion). Let z \in [0,\infty) and t \in [0,T]. To sketch the equation: (r - g(t)) v(t,z) = \pi(t,z) + (\gamma - g(t))v_z(...
This is a follow up to this question. I have mapped from Chebyshev space to the physical space using the mapping $x = ((1-w)\xi^3 - x_p\xi^2 + w\xi + x_p + 1 )*(L/2)$. When in Chebyshev space I have ...
Assume a function $M(t)$ strictly increasing, essentially growing exponentially, and asymptoptically growing at a known rate $\bar{g}$, i.e. $\lim_{t\to\infty}M'(t)/M(t) = \bar{g}$ In a set of awful ...