Skyline matrix

In banded storage, all entries within a fixed distance from the diagonal (called half-bandwidth) are stored.

There is also row oriented skyline storage, and, for symmetric matrices, only one triangle is usually stored.

In addition, the effort of coding skyline Cholesky[3] is about same as for Cholesky for banded matrices (available for banded matrices, e.g. in LAPACK; for a prototype skyline code, see [3]).

Before storing a matrix in skyline format, the rows and columns are typically renumbered to reduce the size of the skyline (the number of nonzero entries stored) and to decrease the number of operations in the skyline Cholesky algorithm.

However, skyline storage is not as popular for very large systems (many millions of equations) because skyline Cholesky is not so easily adapted for massively parallel computing, and general sparse methods,[4] which store only the nonzero entries of the matrix, become more efficient for very large problems due to much less fill-in.