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Weighted Matrix Ordering And Parallel Banded Preconditioners For Iterative Linear System Solvers, Murat Manguoglu, Mehmet Koyuturk, Ahmed Sameh, Ananth Y. Grama

PRISM: NNSA Center for Prediction of Reliability, Integrity and Survivability of Microsystems

The emergence of multicore architectures and highly scalable platforms motivates the development of novel algorithms and techniques that emphasize concurrency and are tolerant of deep memory hierarchies, as opposed to minimizing raw FLOP counts. While direct solvers are reliable, they are often slow and memory-intensive for large problems. Iterative solvers, on the other hand, are more efficient but, in the absence of robust preconditioners, lack reliability. While preconditioners based on incomplete factorizations ( whenever they exist) are effective for many problems, their parallel scalability is generally limited. In this paper, we advocate the use of banded preconditioners instead and introduce …