All Questions
Tagged with computational-physics linear-algebra
16
questions
3
votes
1
answer
890
views
Time and memory required to diagonalize a 18000 by 18000 matrix using numpy in python
Can someone give an estimate of the Time and memory required to diagonalize a 20000 by 20000 complex hermitian matrix using numpy in python ?
- 31
4
votes
1
answer
147
views
Rank-1 correction of matrix exponential
I need to approximate the following in $O(d)$ time for $d\times d$ diagonal $A$ and rank-1 $B$
$$u^T \exp(-A+B) v$$
Here $u,v$ are vectors in $\mathbb{R^+}^d$, $A,B$ are positive semi-definite and $B$ ...
- 2,695
0
votes
0
answers
58
views
Eigenvalues of same operator expressed in two different orthonormal basis are coming out different
I have an operator $H$. I express $H$ as a matrix in the orthonormalized $\{ |e > \}$ basis. Then I diagonalize it to obtain eigenvalues, let's say for example $H$ is $6 \times 6$ and the ...
- 31
2
votes
1
answer
152
views
Numerical diagonalization of Hamiltonian
Framework
I am trying to diagonalize the Bogoliubov-de Gennes Hamiltonian. The problem is that the Hamiltonian contains a Laplacian. This could be solved by using a discretized Laplacian.
How I tried ...
- 21
2
votes
2
answers
1k
views
Diagonalization using LAPACK
Say, we have a Hamiltonian which for simplicity does not mix particle hole sectors. It is just a simple Hamiltonian in real space as shown,
$H=\sum_{ij,\sigma} A(i,j)(c_{i\sigma}^{\dagger}c_{j\sigma} +...
- 23
0
votes
0
answers
52
views
A preconditioner for self-consistent iteration
I tried to derive a preconditioner for self-consistent iteration similar
to section IX in arXiv:0804.2583.
For simplicity, consider here only
one orbital (one or two electrons) systems.
Suppose that ...
- 331
40
votes
23
answers
10k
views
Good examples of "two is easy, three is hard" in computational sciences
I recently encountered a formulation of the meta-phenomenon: "two is easy, three is hard" (phrased this way by Federico Poloni), which can be described, as follows:
When a certain problem is ...
- 8,702
5
votes
1
answer
403
views
How can I apply Euler's Method to predict a point in time rotating around multiple axis'
I am xposting this from my original stackoverflow question where I was presented with a coding challenge that I have been able to narrow down extensively and I think it lies with Euler's Method.
Here'...
- 51
1
vote
1
answer
234
views
Matrix exponential by eigenvectors - implementation issues
I posted a similar question yesterday but I deleted it since I think that I had to reformulate it after some insights.
I want to calculate
$$
\exp(-i\Delta t\,\mathcal{H}) = V\,\mathrm{diag}(\{\exp(-...
- 83
1
vote
1
answer
272
views
Finding the lowest $n$ eigenvalues of a band-diagonal Matrix
I have a real sparse matrix of the form
$$
\left( \begin{array}{ccc}
h_{11} & h_{12} & 0 & h_{14} & & & \\
h_{21} & h_{22} & h_{23} & 0 & h_{25} & & ...
- 417
1
vote
3
answers
166
views
Solving a small non-symmetric, non-diagonally dominant, and non-sparse system
I want to solve a small (20 $\times$ 20 up to 30$\times$30) system which is not symmetric, not diagonally dominant, and not sparse. Each row contains a modified form of the Legendre coefficient of a ...
- 11
1
vote
0
answers
165
views
How to get the eigenvalues of Hamiltonian in an over complete basis
Let $|\psi_i\rangle$, $i=1...N+m$, be a set of overcomplete basis vector in a $N$-dim Hilbert space. The following are known: (Einstein's summation convention assumed)
$$\hat{H}|\psi_i\rangle=H_{ji}|\...
Lagrenge
3
votes
3
answers
4k
views
Understanding Finite-Element Modal Analysis
I am teaching a basic course on computational physics and for the last part of the course I will introduce freshman physics undergraduates to finite-element modelling methods.
I am preparing a COMSOL ...
- 133
1
vote
2
answers
194
views
How to determine the truncation error with products and quotients
If I have an equation given by
$$\displaystyle Y = \frac{a^2}{d^2}\frac{(1-c^2\frac{c}{a})}{(1-b^2)}$$
and I expand $a,b,c,d$ in a Taylor series, where $a$ is truncated at the $A^{th}$ order, $b$ is ...
- 183
1
vote
1
answer
303
views
Solving a linear system whose matrix has imbalanced diagonal entries
I am trying to solve following set of equations:
A(i,i-2)*u(i-2) + A(i,i-1)*u(i-1) + (A(i,i)+β(i) )*u(i) + A(i,i+1)*u(i+1) + A(i,i+2)*u(i+2)= B(i) + β(i)
where i=1:1000000
If values of β varies(...
- 21