All Questions
11,504
questions
0
votes
0
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5
views
Using rust and arpack, getting wrong eigenvalues
I am trying to use arpack to compute eigenvectors in rust. To test things out I made a graph laplacian:
...
0
votes
0
answers
12
views
Projecting the initial state on a Discontinuous Galerkin basis
Context
I want to solve a 1D Burgers equation with a discontinuous Galerkin approach on the space-time domain $(x,t)\in [0,1]^2$. I want to project the function $u(x) = e^{-\frac{(x-0.5)^2}{0.02}}$ ...
4
votes
2
answers
407
views
Solving a generalised eigenvalue problem with non-square matrices
I need to solve a generalised eigenvalue problem of the form
$$A\mathbf{x}=\lambda B \mathbf{x}$$
where $A$ and $B$ are $m \times n$ complex matrices, that are not symmetric with $m>n$.
I am aware ...
2
votes
1
answer
526
views
Overflows and underflows in Python
I’m writing some Python code using NumPy. Since I got an overflow warning, I decided to check for underflows as well at all places in the code, using ...
0
votes
0
answers
17
views
Why does Energy -> temperature conversion failed to converge in my OpenFOAM simulation [closed]
How can I resolve this issue?
I want some help in resolving it. Thanks.
0
votes
1
answer
56
views
How to properly use ARPACK's dsaupd and dseupd?
In Rust, I am trying to solve an eigendecomposition problem through ARPACK. I made the following subroutine for this purpose:
...
0
votes
0
answers
21
views
formula for the elliptical orbit of the magnetic field in a current carrying circular loop [closed]
In a circular current carrying loop the magnetic field lines form elliptical orbits if I have constant value for current and a point let's say at r distance from the center of th current carrying loop ...
0
votes
0
answers
79
views
Guidelines for finding a preconditioner for a matrix that is "near" singular
Given a large non-symmetric non-sparse matrix $A=(a_{m,n})$ with the property that the columns of $A$ are "close", making the matrix very ill-conditioned and near singular. For example, ...
-1
votes
1
answer
68
views
optimal gradient algorithm to determine best $α_k$
Let's consider an optimal-step gradient algorithm and assume that:
$g(α) := f(X_k - α∇f(X_k)) = 2α^2-4α+17$, how can we determine the optimal $α_k$?
Here is my simple solution:
$g(α) = 2α^2-4α+17$
$g'(...
0
votes
1
answer
43
views
step-fixed algorithm first iterates
let us have the fixed-step gradient algorithm, with $p = 2$ and we assume that for $X = (x, y)$,
$∇ f(X) = \begin{pmatrix}
x -1\\
y -2
\end{pmatrix}$
Let me assume we intialize with $X_0 = (0,0)$ what ...
0
votes
1
answer
65
views
step-fixed algorithm to minimize f, which step to ensure convergence?
If we want to apply the fixed-step gradient algorithm to the minimization of $f(x) = \frac{1}{2}(Ax, x)$ where $A$ is a symmetric 2x2 matrix with eigenvalues $\lambda_1 > \lambda_2 > 0$, for ...
1
vote
1
answer
58
views
What are some good medium matrices with known eigenvectors?
I am trying to test if an eigendecomposition I have is working properly. For this I would like some matrices that are 10x10 (ish) with trivial (or known) eigenvectors and eigenvalues so that I can ...
0
votes
0
answers
40
views
conjugate method for minimization of quadratic equations of dim n, upper bound for iterations is n?
Is it true that in the worst case, the conjugate gradient algorithm needs 20 or 21 iterations to converge for the minimization of a quadratic equation of dimension 20? Let's suppose it won't find the ...
0
votes
0
answers
42
views
What techniques are there to take averages and errors in a Monte Carlo simulation in C? Can my code be improved?
I'm trying to perform a Monte Carlo simulation in C and these are the steps I'm following:
We assume an infinite reservoir compound of CO and NO molecules with partial pressures 𝑦CO and 𝑦NO(= 1 − 𝑦...
0
votes
0
answers
33
views
Problems with High-Performance Computing and Stack Exchange Data Explorer. Any Advice? [closed]
I'm currently experiencing some challenges with my high-performance computing setup and a Stack Exchange product. As someone relatively new to managing both hardware and software in this capacity, I ...