All Questions

I need a fast algorithm to perform a specific Fourier-type computation in my physics research. Suppose I have the following two Fourier series in three dimensions $$ a(t_1,t_2,t_3)=\sum_{j=-n}^{n}\...

For a polynomial $C(x)=c_0+\dots+c_n x^n$, consider a circulant matrix $C$ such that $$ C= \begin{pmatrix} c_0 & c_{n-1} & \cdots & c_2 & c_1 \\ c_1 & c_0 &...

The question was already asked here, but doesn't have any meaningful answer, hence I'd like to re-post it. Assuming that we have an algebra with conjugation, we can use Cayley-Dickson construction to ...

All the basic arithmetic operations $\times,+,/,-$ can be parallelized. However continued fraction representation of a rational number is not parallelized. The process of Euclid's algorithm looks ...

Let $R =\mathbb{Z}/N \mathbb{Z}$. Let $f:R\to \mathbb{R}$, $\rho:R\to \lbrack 0,1\rbrack$. We assume that it takes trivial time to compute any given value $f(m)$ or $\rho(m)$. Define $$S(\delta,m) = ...