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1500 questions
13
votes
2 answers
How is the SVD of a matrix computed in practice
How does MATLAB, for instance, calculate the SVD of a given matrix? I assume the answer probably involves computing the eigenvectors and eigenvalues of A*A'. If that is the case, I would also like to know how does it compute those?
olamundo
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13
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3 answers
Optimize an unknown function which can be evaluated only?
Given an unknown function $f:\mathbb R^d \to \mathbb R$, we can evaluate its value at any point in its domain, but we don't have its expression. In other words, $f$ is like a black box to us.
What is the name for the problem of finding the minimizer…
Tim
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13
votes
1 answer
Efficient solution of mixed integer linear programs
Many important problems can be expressed as a mixed integer linear program. Unfortunately computing the optimal solution to this class of problems is NP-Complete. Luckily there are approximation algorithms that can sometimes provide quality…
MRocklin
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13
votes
1 answer
How to construct well-balanced finite volume and discontinuous Galerkin methods for hyperbolic PDEs with source terms?
Source terms, such as those due to bathymetry in the shallow water equations, need to be integrated in a special way in order to preserve physical steady states. Is there a general way to construct well-balanced methods, or does it require special…
Jed Brown
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13
votes
1 answer
Method selection for numeric quadrature
Several families of methods exist for numeric quadrature. If I have a specific class of integrands how do I select the ideal method?
What are the relevant questions to ask both about the integrand (e.g. is it smooth? does it have singularities?)…
MRocklin
- 3,088
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13
votes
5 answers
Repeated nearest neighbor calculation for millions of data points too slow
I have a dataset running into millions of data points in 3D. For the calculation I am doing, I need to calculate neighbor (range search) to each data point in a radius, try to fit a function, calculate the error for the fit, repeat this for next…
Kaustubh Kaluskar
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13
votes
5 answers
Calculation of the sparsity structure for finite element matrices
Question: What methods are available to accurately and efficiently calculate the sparsity structure of a finite element matrix?
Info: I'm working on a Poisson Pressure Equation solver, using Galerkin's method with a quadratic Lagrange basis, written…
John Edwardson
- 133
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13
votes
1 answer
Specialized methods for complex symmetric tridiagonal generalized eigenvalue problems
I have to solve generalized eigenvalue problems $Ax = \lambda Bx$ where $A$ and $B$ are both tridiagonal, $B$ is symmetric positive definite and real, but $A$ is only complex symmetric (not definite or Hermitian). Furthermore, I need the full…
Victor Liu
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13
votes
3 answers
finite volume method: unstructured mesh vs octree adaptation + cell cutting
I'm working with the OpenFOAM C++ Computational Continuum Mechanics library (it can deal with fluid-solid interaction, MHD flows...) which uses arbitrary unstructured meshes. This was driven by the idea of using the advantage of fast generation…
tmaric
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13
votes
5 answers
C++ or Python for a development of CFD library
What would you say would be the advantages/disadvantages of two approaches to coding a general (finite volume, fem, dg) library for Computational Continuum Mechanics? This is how I see things right now, so please provide your own experiences and…
tmaric
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13
votes
2 answers
Strategies for Newton's Method when the Jacobian at the solution is singular
I'm trying to solve the following system of equations for the variables $P,x_1$ and $x_2$ (all else are constants):
$$\frac{A(1-P)}{2}-k_1x_1=0 \\ \frac{AP}{2}-k_2x_2=0 \\ \frac{(1-P)(r_1+x_1)^4}{L_1}-\frac{P(r_1+x_2)^4}{L_2}=0$$
I can see that I…
Paul
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13
votes
3 answers
Understanding the "rate of convergence" for iterative methods
According to Wikipedia the rate of convergence is expressed as a specific ratio of vector norms. I'm trying to understand the difference between "linear" and "quadratic" rates, at different points of time (basically, "at the beginning" of the…
usero
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13
votes
2 answers
What are some good data-types for unstructured cell-centered FVM CFD code?
I'm interested in an advice for efficient data structures for cell browsing in unstructured cell-based finite volume CFD.
One example that I encountered (in dolfyn cfd code) goes like this (I'll show relevant segment)
\begin{listing}
do ip=1,Ncel
…
Johntra Volta
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13
votes
8 answers
Real-world applications of eigendecomposition?
Cross-posted on Math.SE
Are there real-world applications that call specifically for eigenvalues rather than singular values?
I often see eigendecomposition used as "poor-man's SVD"
For instance it's used in Matlab's Lyapunov solver, but that could…
Yaroslav Bulatov
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13
votes
2 answers
Which time-integration methods should we use for hyperbolic PDEs?
If we employ the Method of Lines for discretization (separate time and space discretization) of hyperbolic PDEs we obtain after spatial discretization by our favorite numerical method (fx. Finite Volume Method) does it matter in practice which ODE…
Allan P. Engsig-Karup
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