Weighted Matrix Ordering and Parallel Banded Preconditioners for Iterative Linear System Solvers

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 a reordering strategy that enables their extraction. In contrast to traditional bandwidth reduction techniques, our reordering strategy takes into account the magnitude of the matrix entries, bringing the heaviest elements closer to the diagonal, thus enabling the use of banded preconditi...

• Type: Journal
• Year: 2010
• Where: SIAMSC
• Authors: Murat Manguoglu, Mehmet Koyutürk, Ahmed H. Sameh, Ananth Grama
• Keywords: Effective Banded Solvers, Incomplete Factorization, Preconditioners, SIAMSC 2010