Matrice rare si matrice banda
density = nnz(A)/prod(size(A)) sparsity = 1 -density
% <latex> % O \emph{matrice rar\u{a}} este o matrice a c\u{a}rei raritate este apropiat\u{a} % de 1. \emph{L\u{a}\c{t}imea de band\u{a}} a unei matrice este distan\c{t}a % maxim\{a} de la elementele nenule la diagonala principal\u{a}. % </latex> %
[i,j] = find(A); bandwidth = max(abs(i-j))
%<latex> % differentiable and in fact analytic on $[-1,1]$. (Recall that this means % that for any $s\in [-1,1]$, $f$ has a Taylor series about $s$ that % converges to $f$ in a neighborhood of $s$.) Then without any further % assumptions we may conclude that the Chebyshev projections and % interpolants converge {\bf geometrically}, that is, at the rate % $O(C^{-n})$ for some constant $C>1$. This means the errors will look % like straight lines (or better) on a semilog scale rather than a loglog % scale. This kind of connection was first announced by Bernstein in 1911, % who showed that the best approximations to a function $f$ on $[-1,1]$ % converge geometrically as $n\to\infty$ if and only if $f$ is analytic % [Bernstein 1911 \& 1912{\sc b}]. % </latex>