A is assumed to be a square matrix of order n , but some of the individual routines allow A to be rectangular. The basic task is to compute X , given A and B . The form of the factorization depends on the properties of the matrix A . Band matrices use a compact band storage scheme described in section 5.3.3 . While the primary use of a matrix factorization is to solve a system of equations, other related tasks are provided as well.
Iterative refinement is done in the same precision as the input data.
In particular, the residual is not computed with extra precision, as has been traditionally done. The benefit of this procedure is discussed in Section 4.4 .