Matrix bandwidth
= Matrix bandwidth
{title2=$b=\max\{|i-j|:a_{ij}\ne0\}$}
The bandwidth in this convention is the largest distance from the main diagonal of a nonzero <matrix> entry. A symmetric positive-definite <matrix> of bandwidth $b$ can be factored using $O(Nb^2)$ operations and $O(Nb)$ storage; its <Cholesky decomposition> does not introduce entries outside that band. A variable permutation changes bandwidth, so it is a property of both the sparsity pattern and its ordering.