Parallelization of the Lanczos Algorithm on Multi-core Platforms

In this paper, we report our parallel implementations of the Lanczos sparse linear system solving algorithm over large prime fields, on a multi-core platform. We employ several load-balancing methods suited to these platforms. We have carried out process-level and threadlevel parallel implementations under two different arithmetic libraries, and the best speedup obtained is 6.57 on eight cores. To the best of our knowledge, no implementation of the Lanczos algorithm on a multi-core platform is ever reported in the literature. Moreover, we seem to have achieved significantly larger speedup compared to all previously reported implementations of this algorithm. Key words: sparse linear system, Lanczos algorithm, modular arithmetic, prime field, multi-core machine, parallelization, load balancing

• Type: Conference
• Year: 2010
• Where: ICDCN
• Authors: Souvik Bhattacherjee, Abhijit Das
• Keywords: Distributed Computing, ICDCN 2010, Lanczos Algorithm, Multi-core Platform, Parallel Implementations