Bandmatrix

With band matrix, a matrix is referred to in numerical mathematics, in addition to the main diagonal only a certain number of subdiagonal elements having non-zero. If only a lower and an upper secondary diagonal nonzero then one speaks of tridiagonal matrices. These matrices are so sparse matrices with a specific structure. Banded matrices often arise in the discretization of differential equations.

Description

Be with, the matrix A is a band matrix of bandwidth, if for its elements:

In addition to the main diagonal so only lower p and q upper secondary diagonals are occupied.

Properties

For positive definite band matrices, the band structure is preserved in the Cholesky decomposition. You Spaltenpivotisierung used to solve this applies also for the LU decomposition of a regular band matrix, thereby, only the number of diagonals increases slightly. The cost of the calculation is reduced to each.