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The fast, and The Backward-Stable (left) $3\times 3$ matrix inverse

I need to compute a lot of $3\times3$ matrix inverses (for Newton iteration polar decomposition), with very small number of degenerate cases ($<0.1\%$). Explicit inverse (via matrix minors divided by determinant) seems to work, and is about ~32~40…
Sergiy Migdalskiy
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Implementing std::nextafter: Should denormals-are-zero mode affect it? If so, how?

This might be the wrong stackexchange site for this question. math.SE, cs.SE, programmers.SE, and of course stackoverflow are all possibilities. I'm hoping to reach an audience that might actually use this function, to get some feedback on how…
Peter Cordes
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Communication overhead in supercomputing

I am looking for credible references stating how much resources supercomputers spend on coordinating versus doing actual task-related work. Resources could be available processing power but even Watts seem like a valid unit. I believe one of my…
Tomas Creemers
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MATLAB matrix multiplication (the best computational approach)

I have to make a coordinates transformation between two reference systems (axes). For that, three matrices ($3\times3$) have to be multiplied due to some intermediate axes being used. I have thought about two approaches to resolve this: Method #1:…
julianfperez
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Difference between l2 norm and L2 norm

What is the difference between the $l^2$ norm and the $L^2$ norm. I can not find a definitive reference. Wikipedia uses them interchangeably.
Damascus Steel
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Benchmarks for Gröbner bases and polynomial system solution

In the recent question Solving system of 7 nonlinear algebraic equations symbolically, Brian Borchers experimentally confirmed that Maple can solve a polynomial system that Matlab/Mupad cannot handle. I have heard in the past from people working in…
Federico Poloni
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How to make a good mesh in a biologically accurate model with very small domains

I have been trying to make a biologically accurate 2D spatial model of tissue layers, where different physiological processes happen. This includes mainly chemical reactions, diffusion and fluxes over boundaries. I am making this model in COMSOL…
Dandelion
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Meaning of (meta)heuristic methods

For optimization, from Wikipedia: In computer science, metaheuristic designates a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. Metaheuristics …
Tim
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Calculating Lagrange coefficients for SVM in Python

I'm trying to write a full SVM implementation in Python and I have a few issues computing the Lagrange coefficients. First let me rephrase what I understand from the algorithm to make sure I'm on the right path. If $x_1, x_2, ..., x_n$ is a dataset…
Charles Menguy
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Is there a constrained nonlinear optimization library like IPOPT that runs on GPUs?

Somebody on my team wants to paralelize IPOPT. (at least some of functions of it). I have not been able to find a GPU implementation of it or a similar package. Nor I've found anything on their docs. So the question is, is there an alternative…
cauchi
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How to derive an Implicit Runge-Kutta method from Pade approximation

I was reading some work by Butcher and I came across Pade approximations and the correlation between them and stability functions for some Implicit Runge-Kutta methods. For example, in this Pade table for the exponential function, we see that the…
Matthew Cassell
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C++ library for numerical intergration (quadrature)

I have my own little subroutine for numerical integration (quadrature), which is a C++ adaptation of an ALGOL program published by Bulirsch & Stoer in 1967 (Numerische Mathematik, 9, 271-278). I would like to upgrade to a more modern (adaptive)…
Walter
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Matching Similar Items from a Set

I'm trying to match items. Given a set of $n$ items I can rank on a scale from 0 to 100 of how similar they are to one another. For instance, if item $n_1$ is milk and item $n_2$ is also milk, then the similarity between $n_1$ and $n_2$ would be…
Jason
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Calculating the log-determinant of a large sparse matrix

I need to calculate $\log(\det (\mathbf M_i))$ where the $\mathbf M_i$'s are large sparse matrices, which are real, symmetric and positive semi-definite. I hope to have between $10$ and $100$ of those. Physically, each $\mathbf M_i$ is the…
yohbs
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Time advance in Adaptive Mesh Refinement method

I am working on solving complex system of 2D PDEs governing the behaviour of plasma in a gas lamp during discharge. Recent tests have shown that because of steep gradients in temperature field and overall explosive nature of a process I won't go…
Dantragof
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