Questions tagged [derivative]
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11 questions
1
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1
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70
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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
155
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
23
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
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1
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92
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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
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0
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45
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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
1k
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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
$$
f(x) = \exp(-10(x-1)^2) ,\, \, x \in [0,2]
$$
...
- 852
3
votes
1
answer
298
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
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1
answer
163
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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
284
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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
96
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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 ...
- 852