Version 1.0.2

28th March 2013

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MA65 Unsymmetric banded system of linear equations

To solve an unsymmetric banded system of linear equations. Given a unsymmetric band matrix A = {aij}n×n and an n-vector b, this subroutine solves the system Ax = b.

The matrix is factorized using Gaussian elimination with row interchanges. If the lower semibandwidth is kl and the upper semibandwidth is ku, that is, if aij = 0 for i > j + kl or j > i + ku, fill-in is limited to kl additional diagonals of the upper triangle and the computation is performed within an array of size n(2kl + ku + 1). At each pivotal step, operations are avoided on any row with a zero in the pivot column and on the columns beyond the last to have an entry in the pivot row.