Editing Band matrix (section)

==Applications==
In [[numerical analysis]], matrices from [[finite element]] or [[finite difference]] problems are often banded. Such matrices can be viewed as descriptions of the coupling between the problem variables; the banded property corresponds to the fact that variables are not coupled over arbitrarily large distances. Such matrices can be further divided{{snd}}for instance, banded matrices exist where every element in the band is nonzero. 

Problems in higher dimensions also lead to banded matrices, in which case the band itself also tends to be sparse. For instance, a partial differential equation on a square domain (using central differences) will yield a matrix with a bandwidth equal to the [[square root]] of the matrix dimension, but inside the band only 5 diagonals are nonzero. Unfortunately, applying [[Gaussian elimination]] (or equivalently an [[LU decomposition]]) to such a matrix results in the band being filled in by many non-zero elements.