BABDCR- Bordered Almost Block Diagonal Cyclic Reduction algorithm
BABDCR is a package of Fortran 90 subroutines for the solution of linear systems with Bordered Almost Block Diagonal (BABD) structure
that is having a block upper bidiagonal structure with an additional block in the right--upper corner with each block Ba, Bb Si and Ri of the same dimension mxm.
The algorithms implemented perform cyclic reduction as described in [1],[3] of the coefficient matrix in order to reduce fill-in due to the corner block.
Some test and comparisons with other linear solvers as COLROW, SOLVEBLOK, RSCALE are presented in [3],[4].
A general BABD linear system can be solved with a modification of the BABDCR package, see [2].
A parallel implementation of BABDCR using Message Passing MPI has been also developed [4].
Dr. Giuseppe Romanazzi – Departamento de Matemática, Universidade de Coimbra, Portugal
Prof. Pierluigi Amodio – Dipartimento di Matematica, Università degli studi di Bari, Italy
BABDCR package download.
After downloading the package, consult the files read_me_first.txt and babdcr_note.txt. These files are also listed here read_me_first, babdcr_note.
GBABDCR download. GBABDCR solves General BABD linear systems
PARABABDCR [4] download, solves BABD linear systems using a MPI parallel implementation of BABDCR.
[1] Amodio, P., and Romanazzi, G., Algorithm 859: BABDCR: a Fortran 90 package for the Solution of Bordered ABD Linear Systems, ACM Transactions on Mathematical Software, 32, 4, 597—608 (2006)
[2] P.Amodio, I. Gladwell, and G. Romanazzi, Numerical Solution of General Bordered ABD Linear Systems by Cyclic Reduction, JNAIAM (Journal of Numerical Analysis, Industrial and Applied Mathematics), 1, 1, 5--12 (2006)
[3] Phd Thesis: G.Romanazzi, Numerical Solution of BABD linear systems arising from BVPs, Università degli studi di Bari (2006)
[4] Amodio, P., Gladwell I., Romanazzi, G., An algorithm for the solution of Bordered ABD linear systems arising from Boundary Value Problems, Multibody Dynamics 2007, ECCOMAS Thematic Conference, C.L. Bottasso, P.Maserati, L.Trainelli (eds), Milano, Italy, 25-28 June 2007
We acknowledge the contributions of users that have reported bugs.