ScaLAPACK user's guide
A Fast Direct Solution of Poisson's Equation Using Fourier Analysis
Journal of the ACM (JACM)
A Comparison of Parallel Solvers for Diagonally Dominant and General Narrow-Banded Linear Systems II
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Analysis of the Truncated SPIKE Algorithm
SIAM Journal on Matrix Analysis and Applications
Parallel solution of narrow banded diagonally dominant linear systems
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
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The ScaLAPACK library contains a pair of routines for solving banded linear systems which are strictly diagonally dominant by rows. Mathematically, the algorithm is complete block cyclic reduction corresponding to a particular block partitioning of the system. In this paper we extend Heller's analysis of incomplete cyclic reduction for block tridiagonal systems to the ScaLAPACK case. We obtain a tight estimate on the significance of the off diagonal blocks of the tridiagonal linear systems generated by the cyclic reduction algorithm. Numerical experiments illustrate the advantage of omitting all but the first reduction step for a class of matrices related to high order approximations of the Laplace operator.