Yamazaki I., Wu K. (2012) A Communication-Avoiding Thick-Restart Lanczos Method on a Distributed-Memory System. In: Alexander M. et al. (eds) Euro-Par 2011: Parallel Processing Workshops. Euro-Par 2011. Lecture Notes in Computer Science, vol 7155. Springer, Berlin, Heidelberg
The Thick-Restart Lanczos (TRLan) method is an effective method for solving large-scale Hermitian eigenvalue problems. On a modern computer, communication can dominate the solution time of TRLan. To enhance the performance of TRLan, we develop CA-TRLan that integrates communication-avoiding techniques into TRLan. To study the numerical stability and solution time of CA-TRLan, we conduct numerical experiments using both synthetic diagonal matrices and matrices from the University of Florida sparse matrix collection. Our experimental results on up to 1,024 processors of a distributed-memory system demonstrate that CA-TRLan can achieve speedups of up to three over TRLan while maintaining numerical stability.