# Questions tagged [approximation]

For questions that involve concrete approximations, such as finding an approximate value of a number with some precision. For questions that belong to the mathematical area of Approximation Theory, use (approximation-theory).

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### Low-dimension matrix approximation?

I have a matrix $\mathbf E_1 \in \mathbb R^{m\times n_1}$. I would like to approximate it with a matrix $\mathbf E_2 \in \mathbb R^{m\times n_2}$ with $n_2 < n_1$, where "approximate" ...
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### Assumptions made in Liouville-Green Approximation

Question: Consider $y'' + \frac{1-x}{x^3} y = 0$ Derive the first three terms in Liouville Green approximation. Hence obtain corresponding asymptotic approximations as x → ∞ of two linearly ...
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### Approximating $\#\{\pi \in S_n:\exists k,\pi(k)=k,~k\leq m\}$
Consider the permutations from $S_n$ and let $$K(n,m)=\#\{\pi \in S_n:\exists k,\pi(k)=k,~k\leq m\}$$ be the number of such permutations which have a fixed point in the first $m$ positions. I am ...