Selected Publications

Unpublished Software

The directory leq contains some unpublished software for solving almost block diagonal linear systems, tridiagonal systems and block tri-diagonal systems.

complexcolrow.f is a complex version of the software package COLROW, available as TOMS/603 at netlib. The double precision complex version is in complexcolrowd.f.

colrow.f is a modified version of COLROW which can solve the system ATx = b, after first performing the Gauss Factorization of A, using the same algorithm as COLROW. This facilitates a condition number estimation, using the procedure of Nick Higham, in TOMS/674. The condition umber estimator is given in condcolrow.f

Matlab versions of the colrow codes and the condition number estimator can be found in colrowm . These were written as part of an MSc thesis by Rania Ghanam, Dalhousie University, January 2007.

The code lampak.f is an alternative approach to the factorization of almost block diagonal systems.

The package ABDPACK, (TOMS/704), solves systems of the form Ax = b, where A has a special structure arising from collocation at Gauss points. In order to provide a way of estimating the condition number of A the code was modified to handle ATx = b. This modified software, and the subroutine DONEST (a double precision version of TOMS/674) is in abdcnd.f. A short report on this work is in a technical report. This package was developed by an Honours student, Roderick Alexander Affleck, BSc 1997, for his Honours thesis Condensation of Almost Block Diagonal Matrices in Monomial Spline Collocation of Parabolic Differential Equations.

The block-tridiagonal codes are in the sub-directory block-tri-diag.

Some related work on tridiagonal systems by Graeme Fairweather can be found here.