Questions tagged [derivative]
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13 questions
1 vote
0 answers
79 views
Numerical recipes for eliminating edge effects in calculating integer and fractional derivatives with FFT
The introduction of edge effects (Gibbs oscillations) is a well-known effect in discrete Fourier transform based derivatives. Suppose we have a time series which has signal of interest on the edges as ...
- 111
4 votes
1 answer
249 views
Chebyshev Series Derivative in terms of Coefficients
We all learned in Calc 1 how to take derivatives of polynomials. What we were probably not told, is that this is but one possible expression of a function, in terms of a "power series", and ...
- 181
1 vote
1 answer
91 views
Pade discretization for the first derivative
I am looking for the coefficients a,alpha,beta,gamma for highest possible order of first derivative approximation in the following scheme. $u_x$ denotes first derivative with respect to $x$ and $i$ ...
- 111
2 votes
1 answer
189 views
Looking for a numerical algorithm or library to calculate derivatives of degenerate eigenvalues
There is a well known result to easily calculate the derivative of non degenerate eigenvalues : $$ v_p^T \frac{dA}{dx} v_p = \frac{de_p}{dx} \space\space \space(1)$$ But when they are degenerate, how ...
- 151
1 vote
0 answers
29 views
Calculating Gradients in a workflow involving rasterization and image/polygon transformation
I have an odd little problem facing me for my project. I have a smooth polygon defined by parameters. I have convolution transformation, similar to a Gaussian blur. This transformation can only be ...
- 11
0 votes
1 answer
133 views
Derivative using torch.fft oscilates on the boundary
I was trying to use the torch.fft to compute derivatives. The issue is that even for a simple example ($f = \sin(x)$), I have weird oscillations on the boundaries. ...
- 35
0 votes
0 answers
58 views
Transformation matrix for global displacements derivates to local ones
The derivatives of the displacements in the coordinate system $\bar{x} \bar{y} \bar{z}$ is given by \begin{equation} \begin{aligned} \{\bar{L}\} & = \begin{Bmatrix} ...
- 294
3 votes
2 answers
2k views
compute accurate derivatives using FFT
I'm trying to learn how to compute accurate derivatives using the FFT. In the code at the end of this question I'm trying to compute derivatives of $$ f(x) = \exp(-10(x-1)^2) ,\, \, x \in [0,2] $$ ...
- 908
3 votes
1 answer
348 views
How to evaluate the points near/at the boundary when using Richardson extrapolation for improved accuracy of a derivative
If we want to improve the accuracy of our numerical estimation of a derivative, we can use Richardson extrapolation. The method is very beneficial when using a centered difference scheme and the ...
4 votes
1 answer
176 views
Is there a software package that can compute the 1-dimensional preimage of a point?
I have a smooth function $F: \mathbb{R}^n \to \mathbb{R}^{n-1}$ and points $x_0, y_0$ with $F(x_0) = y_0$. For theoretical reasons, I know that $y_0$ is a regular value of $F$, which means that the ...
- 255
0 votes
2 answers
2k views
When can I use finite differences for differentiation?
Finite differences are usually used to integrate ODE's and PDE's. However, sometimes they can be used for differentiation which I illustrated simply by using the Matlab code below to differentiate the ...
3 votes
1 answer
324 views
Finite difference problem
I have a problem to resolve with the Finite Difference method in $[a,b]$: $$-\frac{d}{dx}(\alpha(x)\frac{du}{dx})= g(x),$$ with $\alpha(x) \in L^{\infty}$ continuous in $]a,c[$ and $]c,b[$ and ...
- 31
1 vote
1 answer
120 views
derivative matrix and the Dirac delta distribution
For a project I'm working on, I was working with the following equation $$ w(x) = \int k(x,y)v(y)dy $$ I noticed that if I choose $$ k(x,y) = -\delta'(x-y) $$ Then we probably get (I haven't touched ...
- 908