MA65 — Unsymmetric banded system of linear equations

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 $A = {a_{i j}}_{n \times n}$ and an $n$ -vector $b$ , this subroutine solves the system $A x = b$ .

The matrix is factorized using Gaussian elimination with row interchanges. If the lower semibandwidth is $k l$ and the upper semibandwidth is $k u$ , that is, if $a_{i j} = 0$ for $i > j + k l$ or $j > i + k u$ , ﬁll-in is limited to $k l$ additional diagonals of the upper triangle and the computation is performed within an array of size $n (2 k l + k u + 1)$ . 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.