Most Popular
1500 questions
9
votes
2 answers
How do Volkov and Demmel experimentally determine the latencies, line sizes, and page sizes of a GPU?
In "LU, QR and Cholesky Factorizations using Vector Capabilities of GPUs", by Vasily Volkov and James Demmel, there is an interesting way to interpret the latencies, line sizes, and page sizes of a cache from a graph like this:
Apparently, the line…
John Hoffman
- 193
- 3
9
votes
4 answers
Sparse matrix implementation of the Kalman Filter?
I have a Kalman Filter based modelling code that I have developed for a near-real time regional ionospheric mapping application. The code assimilates data from different sensors into a map (described by a set of basis functions) using a Kalman…
Bogdanovist
- 287
- 2
- 6
9
votes
1 answer
How to approximate the condition number of a large matrix?
How do I approximate the condition number of a large matrix $G$, if $G$ is a combination of Fourier transforms $F$ (non-uniform or uniform), finite differences $R$, and diagonal matrices $S$?
The matrices are very large and not stored in memory and…
Stiefel
- 245
- 2
- 5
9
votes
3 answers
Iterative methods for indefinite systems without block structure
Indefinite systems of matrices appear for example in the discretization of saddle point problems by mixed finite elements. The system matrix can then be put in the form
$$\begin{pmatrix} A & B^t \\ B & C\end{pmatrix}$$
where $A$ is negative…
shuhalo
- 3,660
- 1
- 20
- 31
9
votes
1 answer
Well-posedness of a linear elasticity problem with periodic boundary conditions
For certain applications, such as steady state heat transfer and flow in porous media, it is possible to simulate a much larger (infinite) domain by imposing periodic boundary conditions on opposite boundary faces and dirichlet bc's on the remaining…
Paul
- 12,045
- 7
- 56
- 129
9
votes
2 answers
Parallel computation of big covariance matrices
We need to compute covariance matrices with sizes ranging from $10000\times10000$ to $100000\times100000$. We have access to GPUs and clusters, we wonder what is the best parallel approach for speeding up these computations.
Open the way
- 711
- 1
- 9
- 15
9
votes
1 answer
large dense low rank assignment problem
Is there a reasonably cheap method to solve the large, dense, low rank assignment problem $\max_\pi \sum_i A_{\pi i,i}$, where $\pi$ runs over all permutations.of $1:n$?
Here $A$ is an $n\times n$ matrix of low rank $r$. Typical sizes would be …
Arnold Neumaier
- 11,318
- 20
- 47
9
votes
1 answer
What is the most accurate interpolation method for a 3D-flowfield on a structured grid?
I solve multi-species, compressible Navier-Stokes equations on a 3D structured grid. I have obtained a solution on a given grid (let's say a relatively coarse one). I want now to refine my grid and interpolate my previous solution on my new grid…
FrenchKheldar
- 1,308
- 1
- 9
- 22
9
votes
1 answer
Numerical integration for modelling curve for superconductors (Python)
I am a physicist who is trying to model the current-voltage characteristics of a superconductor-superconductor junction.
The equation for this model is:
\begin{align}
I(V) = \frac{1}{eR_{\mathrm{n-n}}}\int_{-\infty}^{\infty}\frac{|E|}{[E^{2} -…
query
- 91
- 2
9
votes
4 answers
Order of MATLAB FFT frequencies
This wikibook states that the output of MATLAB's FFT corresponds with the wavenumbers ordered as:
$$k=\left\{0,1,...,\frac{n}{2},-\frac{n}{2}+1,-\frac{n}{2}+2,...,-1\right\}$$
However, in the example codes on the same page, the wavenumbers are coded…
Doubt
- 423
- 4
- 10
9
votes
1 answer
preconditioner for a matrix-free method to solve Ax=b
I need to solve Ax=b, but I realize that even if it is sparse, storing the matrix coefficients of my problem will take too much memory.
So now I'm considering using a matrix-free method, because the same coefficients appear a lot of time in the…
nat chouf
- 353
- 2
- 10
9
votes
2 answers
Optimization method that considers varying time cost of objective function for different parameters
I am working on improving the optimization process of some demographic modeling software so it can better fit demographic models to data. We'd like to decrease optimization time.
The time it takes to evaluate our objective function varies a lot,…
nova
- 191
- 4
9
votes
2 answers
discrete $L^p$ norms for non-uniform grid
I am reading a book on numerical methods and the square of the discrete $L^2$ norm is defined as $$||x||^2_2=h\sum_1^Nx^2_i$$
Every point gets a "weight", which is $h$, thus this is like an average over the squares of the values at all points. This…
Kamil
- 1,206
- 11
- 23
9
votes
4 answers
When we use Bernstein polynomials in application
When it is preferable to use Bernstein polynomials to approximate a continuous function instead of using the only following preliminary Numerical Analysis methods: "Lagrange Polynomials", "Simple finite differences operators".
The question is about…
AmirHosein Sadeghimanesh
- 193
- 2
- 7
9
votes
1 answer
Hybrid spatial schemes for CFD: any downside to blending versus switching?
Aside from extra computational cost due to having to compute both fluxes over a certain region, is there any downside to blend two flux evaluations for a hybrid scheme in a finite volume method? The flux evaluation would look like…
FrenchKheldar
- 1,308
- 1
- 9
- 22