Questions tagged [derivative]
The derivative tag has no usage guidance.
9
questions
4
votes
1
answer
162
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
3
votes
2
answers
1k
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
$$
f(x) = \exp(-10(x-1)^2) ,\, \, x \in [0,2]
$$
...
- 832
3
votes
1
answer
280
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
3
votes
1
answer
281
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 ...
1
vote
1
answer
90
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 ...
- 832
1
vote
0
answers
21
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
2
answers
2k
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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 ...
0
votes
1
answer
81
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
38
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}
...
