Matrices with a small number of nonzero entries are called sparse matrices. Sparse matrices occur, for example, in scientific computing when describing discrete differential operators in the context of numerically solving partial differential equations.

Sparse matrices often have large dimensions, sometimes so large that the entire matrix (with zero entries) would not even fit in the available memory. This is one motivation for a special type for sparse matrices. Another motivation is better performance of operations where zero matrix entries can be avoided.

There are only a very limited number of algorithms for general, unstructured sparse matrices in linear algebra. Most of them are iterative in nature and based on efficient implementations of matrix-vector multiplication for sparse matrices.

Examples for sparse matrices are diagonal or banded matrices. The simple pattern of these matrices allows straightforward storing strategies; the principal diagonal and the sub- and super...