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Good examples of "two is easy, three is hard" in computational sciences

MaxEnt distribution subject to equality constraints on cumulants is easy to compute for constraints on first 2 cumulants (closed form solution), hard for constraints on first 3 cumulants. In the ...
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1 vote

Good examples of "two is easy, three is hard" in computational sciences

The non-negative rank of an entrywise non-negative matrix $A\in\mathbb{R}^{m\times n}_{\geq 0}$, i.e., the minimum $r$ for which a factorization $A = BC$ exists with $B\in\mathbb{R}^{m\times r}_{\geq ...
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Column-normalized inverse?

$ \def\m#1{\left[\begin{array}{r}#1\end{array}\right]} \def\e{\epsilon} \def\qiq{\quad\implies\quad} \def\LR#1{\left(#1\right)} \def\Diag#1{\operatorname{Diag}\left(#1\right)} $Construct the ...
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  • 389
2 votes

Largest singular value without using the adjoint

You could use the characterization $$ \sigma_{\max} = \max_{\dim S = 1} \min_{x \in S} \frac{||Ax||_2}{||x||_2} $$ Creating random vectors $x$ and computing the norm of $||Ax||_2$ will give an ...
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  • 547
2 votes

Good examples of "two is easy, three is hard" in computational sciences

Given an integer N, it's easy enough to find m,n so that mn=N and ...
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Good examples of "two is easy, three is hard" in computational sciences

Predicting the behaviour of a pendulum is comparatively easy. For the simplification of a mathematical pendulum we know the analytic solutions and the numerical simulation of a single pendulum is ...
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2 votes
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Numerical representation of linear spaces

This sounds like an exercise in semiotics, but I'll try all the same. One alternative representation scheme for the particular case of the space of continuous functions on some n-dimensional domain $\...
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