Matrix bandwidth ($b=\max \{|i-j|:a_{ij}\ne 0\}$)

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 $O(N{b}^2)$ 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.