The explicit Spike algorithm : Iterative solution of the reduced system

The explicit Spike algorithm applies to narrow banded linear systems which are strictly diagonally dominant by rows. The parallel bottleneck is the solution of the so-called reduced system which is block tridiagonal and strictly diagonally dominant by rows. The reduced system can be solved iteratively using the truncated reduced system matrix as a preconditioner. In this paper we derive a tight estimate for the quality of this preconditioner