Questions tagged [l2-norm]
The l2-norm tag has no usage guidance.
16
questions
3
votes
1
answer
148
views
How to compute numerically the $H^{1/2}$ norm of a function
I'm, in the context of FEM. Let's say I have a discrete function $g$ living on the boundary of my domain $D$. I need to compute numerically $||g||_{1/2,\partial D}$.
The definition I know is the ...
- 261
0
votes
0
answers
33
views
Difference between minimizing a function by gradient descent and by norm minimization?
I have working on 2 ways of training a neural network. The first method uses gradient descent updates the model with Adam optimizer. the second method minimizes the norm of the gradient of the ...
- 113
0
votes
1
answer
78
views
Does the loss function in a deep neural network act as a norm?
I read somewhere that the Measn squared error loss function acts as L2 norm of the paramter vector. I would like to know if I am using binary cross entropy loss function, do I need to calculate the ...
- 113
1
vote
2
answers
203
views
Finding weighted average of curves
This is related to my previous post here
I have a dataset with values of multiple curves. An example plot is shown below.
I want to scale the curves (move up/down) so that all curves overlap.
The ...
- 491
4
votes
4
answers
639
views
Minimize distance between curves
I have a dataset with values of multiple curves. An example plot is shown below.
I want to shift the curves (up/down) so that all curves overlap. This would mean the data points in each curve is ...
- 491
1
vote
1
answer
341
views
2-norm and infinty norm of a system in controls
How to compute 2-norm or infinity norm of following system?
i am confused whether to calculate using simple matrix theory "where it don't regard for s domain" or H2 and H-infinty norm. ...
- 31
1
vote
0
answers
133
views
Weak form of Elliptic problem with mixed Dirichlet & Neumann conditions
Let $\Omega \subset \mathbb{R}$ in a bounded polygon domain and $f:\Omega \to \mathbb{R}$ known function.We split the boundary into two parts $\partial \Omega_{1}$ and $\partial \Omega_{2}$ such that $...
user38211
1
vote
1
answer
200
views
Frobenius norm of a binary matrix
In term of the mathematical distance measurement,
What is the significance of a Frobenius norm for a binary matrix?
- 31
3
votes
1
answer
718
views
About the discrete $H^1$ norm
I need to understand what is the right expression for the "discrete $H^1$-norm of a function v(which of course need to be in $H^1$).
By definition, $$||v||_{H^1}^2 = ||\nabla v||_{2}^2 + ||v||_2^2 $$
...
- 299
5
votes
1
answer
624
views
Fastest way to calculate the $2$-norm (or an upper bound for the $2$-norm) of the inverse of a matrix $A\in \mathbb{C}^{N\times N}$
I have a matrix $A\in \mathbb{C}^{N\times N}$ and I need to calculate $||A^{-1}||_{2}$ efficiently. Can it be done without having to evaluate the inverse explicitly?
In general, I am looking for ...
- 153
1
vote
1
answer
608
views
How I could calculate L2 norm of an unstructured grid?
I want to calculate L2 norm of a 3D unstructured grid to compare my simulation results in two different mesh sizes as coarse and fine. I read this answer and it seems in three-dimensional space, I ...
- 2,322
1
vote
0
answers
150
views
computing dual matrix trace norm and tensor gradient in python
I'm trying to write the following function in python:
$$
f_\mu(\mathcal X) = f_0(\mathcal X) + \sum_{i = 1}^n \max_{||\mathcal Y_{i(i)}|| \leq1} \alpha_i\langle \mathcal X_{(i)},\mathcal Y_{i(i)} \...
- 11
6
votes
2
answers
593
views
Residual norm of PDE discretization: correspondence in the continuous problem?
Solving a linear PDE like
$$
\Delta u = f \quad\text{on } \Omega,\\
n\cdot \nabla u = 0 \quad\text{on } \Gamma,
$$
with Finite Elements usually goes like this:
Create the discretization $Au=b$ via
$$
...
- 3,108
1
vote
0
answers
419
views
Estimate $L_2$ norm of a elliptic problem with unknown exact solution on finite element method
I have the elliptic problem $$-\Delta u = 1,\,\,\Omega\subset\mathbb{R}^2$$
with $u=0$ on $\partial\Omega,$ with $\Omega=[-1,1]^2\backslash([0,1]\times[-1,0])$ and I want to estimate the $L_2$ error ...
- 145
4
votes
1
answer
908
views
$L^2$-error in FEM: how to compute integral over reference element?
I have the following problem. The domain is $(0,1)$ and we consider a uniform triangulation on $\hat{\Omega}$ with elements $K_i = [i/N,(i+1)/N]$ and $X_h^1$ the linear finite element space. I wrote ...
- 404
1
vote
1
answer
581
views
Physical interpretation of L2 norm of heat equation solution
For the heat equation
\begin{equation}
u_t(t,x) = \nu u_{xx}(t,x)
\end{equation}
for $x \in [0,1]$ with boundary conditions $u(t,0) = u(t,1) = 0$ and initial value $u(0,x) = u_0(x)$ it is easy to ...
- 1,238