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1500 questions
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Stability criterion for waves in anisotropic solids

The equations of motion for an elastic solid are given by $$\begin{align} &\nabla \cdot \boldsymbol{\sigma} + \mathbf{f} = \rho \ddot{\mathbf{u}}\\ &\boldsymbol{\sigma} = \mathbb{C}\boldsymbol{\varepsilon}\\ &\boldsymbol{\varepsilon} =…
nicoguaro
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Choosing how many iterations to use in VEGAS

I'm using VEGAS integration, specifically the GSL implementation, for some QCD calculations, and I've been investigating the behavior of the algorithm for various numbers of iterations in an attempt to get more accurate results. The value produced…
David Z
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Incremental SVD implementation in MATLAB

Is there any library/toolbox which has implementation of incremental SVD in MATLAB. I have implemented this paper, it is fast but does not work well. I tried this but in this also error propagates fast (within updating 5-10 points error is high).
Parag
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Compute eigenvectors of a matrix with known eigenvalue spectrum

If I have already accurately known the eigenvalue spectrum (i.e. all eigenvalues) of a matrix, is there any efficient numerical algorithm to compute all the eigenvectors corresponding to these eigenvalues? I guess with the information about…
Enchantedland
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Potential Reduction and Primal Path following methods

In both the potential reduction and primal path following interior point methods for linear programming, a barrier function is constructed which contains the terms $-\sum \log x_j$ where $x_j$ are the variables. This is to keep the variables from…
Opt
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Newton iteration for cube root without division

It's a fairly well known trick to avoid division in calculating square-roots to apply Newton's method to finding $1/\sqrt{x}$, and probably better known, using Newton's method to find reciprocals without division. In rescuing a StackOverflow thread…
hardmath
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Good tutorials on how to use Butcher tables?

I tried to go to the primary sources in order to understand how to use Butcher tables to simplify the algebra I need to do when using Taylor series to find the order of accuracy of a scheme, for instance. However, maybe because of a lack of relevant…
bzm3r
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Projecting Finite Element solution onto new mesh

I am implementing a finite element solver in MATLAB and I have the following problem. Let's say I have a mesh $\mathcal{T}_1$ with triangular elements on a rectangular domain $\Omega\subset\mathbb{R}^2$. I know the positions of all the nodes on the…
Eff
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How many Fourier magnitudes do I have to calculate before an FFT becomes more efficient than a DFT?

I need to compute only a small number of low frequency Fourier components of a complex 2-dimensional array. I'll be computing the same Fourier components over and over again as the input array changes. Clearly, in the limit where I only want one…
Colin K
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How does a Sparse Direct Solver know about dimensionality of a problem being solved?

It is claimed that the time and memory complexities of sparse direct solver are $O(N^2)$ and $O(N^{4/3})$ for 3D problems and $O(N^{1.5})$ and $O(N \log N)$ for 2D, respectively. But how does a general-purpose direct solver know about…
Alexander
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diagonalization of matrix - omitting small matrix elements

I was wondering whether there is some theorem that allows me to put an upper bound on the error introduced by omitting small matrix elements from a matrix before diagonalization. Let's assume we have a large matrix, whose matrix elements range from…
ftiaronsem
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calculating eigenvector components of a given vector

I have some vector $V$ which can be decomposed into the eigenspace of the hermitian sparse operator $M$: $V = \sum_i v_i \hat{m}_i$ Is there a way to find the $\hat{m}_i$ (the eigenvector itself) that correspond to the largest $v_i$ (in…
Andrew Spott
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Reference Request for Profiling High Performance Computing Codes

I write codes in Fortran and C for various matrix algorithms. However, when I profile my codes using VTune, I usually run into some terminology that I cannot fully appreciate. Is there a good resource for learning profiling from scratch to a fairly…
Inquest
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Quick and simple discrete 2D Helmholtz-Hodge Decomposition using FFTs?

For a silly screen saver I'm trying to develop, I'd like to randomly generate a divergence-free 2D array of 2D vectors, and then use it to generate a line integral convolution plot. I've heard$^1$ that one way to do this is to generate random noise,…
DumpsterDoofus
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On the completeness of the Periodic Table of Finite Elements

In a recent SIAM News article, there is a long article describing a systematic organization of the finite elements, aptly dubbed the Periodic Table of Finite Elements. Its really quite fascinating to see how classification can be accomplished via…
Paul
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