THE PARALLEL QR FACTORIZATION ALGORITHM FOR TRIDIAGONAL LINEAR-SYSTEMS

We describe a new parallel solver in the class of partition methods fo r general, nonsingular tridiagonal linear systems. Starting from an al ready known partitioning of the coefficient matrix among the parallel processors, we define a factorization, based on the QR factorization, which depends on the conditioning of the sub-blocks in each processor. Moreover, also the reduced system, whose solution is the only scalar section of the algorithm, has a dimension which depends both on the co nditioning of these sub-blocks, and on the number of processors. We an alyze the stability properties of the obtained parallel factorization, and report some numerical tests carried out on a net of transputers.