The tag has no wiki summary.

learn more… | top users | synonyms

5
votes
1answer
294 views

Sparse approximate representation of a collection of vectors

Suppose I have a collection of $n$ vectors $C \subset \mathbb{F}_2^n$. They are of course spanned by the canonical set of $n$ basis vectors. What I would like to find is a much smaller (~ $\log n$) ...
3
votes
2answers
866 views

Variant of Fermat's last theorem

By Fermat's last theorem, the equation $u^3+v^3=w^3$ has no solutions in positive integers $u,v,w$. Now consider the following variant : call $\rho(x)$ the distance between $x$ and the nearest ...
11
votes
6answers
3k views

Solving NP problems in (usually) Polynomial time?

Just because a problem is NP-complete doesn't mean it can't be usually solved quickly. The best example of this is probably the traveling salesman problem, for which extraordinarily large instances ...
4
votes
1answer
419 views

Interpolation by a function whose second derivative is bounded

I don't know if this is an easy question for specialists in the field. Consider the following interpolation problem : let $\varepsilon >0$, $X$ be a finite set of real numbers and $g$ be a ...
8
votes
3answers
635 views

Approximating with translated Gaussians and low-frequency trig functions

Defining the translated Gaussians by $f_t(x)=\exp(-(x-t)^2)$ for $t,x\in\Bbb{R}$, we showed that the linear span of $\{f_t \mid 0 \le t < \epsilon\}$ is dense in $L^2(\Bbb{R})$, for any ...