## SYNOPSIS

- SUBROUTINE PSGBTRF(
- N, BWL, BWU, A, JA, DESCA, IPIV, AF, LAF, WORK, LWORK, INFO )

- INTEGER BWL, BWU, INFO, JA, LAF, LWORK, N

- INTEGER DESCA( * ), IPIV( * )

- REAL A( * ), AF( * ), WORK( * )

## PURPOSE

PSGBTRF computes a LU factorization of an N-by-N real banded distributed matrix with bandwidth BWL, BWU: A(1:N, JA:JA+N-1). Reordering is used to increase parallelism in the factorization. This reordering results in factors that are DIFFERENT from those produced by equivalent sequential codes. These factors cannot be used directly by users; however, they can be used insubsequent calls to PSGBTRS to solve linear systems.

The factorization has the form

P A(1:N, JA:JA+N-1) Q = L U

where U is a banded upper triangular matrix and L is banded
lower triangular, and P and Q are permutation matrices.

The matrix Q represents reordering of columns

for parallelism's sake, while P represents

reordering of rows for numerical stability using

classic partial pivoting.