Multiple Explicitly Restarted Arnoldi Method for Solving Large Eigenproblems

Nahid Emad, Serge Petiton, Guy Edjlali
2005 SIAM Journal on Scientific Computing  
In this paper we propose a new approach for calculating some eigenpairs of large sparse non-Hermitian matrices. This method, called Multiple Explicitly Restarted Arnoldi (MERAM), is particularly well suited for environments that combine different parallel programming paradigms. This technique is based on a multiple use of Explicitly Restarted Arnoldi method and improves its convergence. This technique is implemented and tested on a distributed enviromnment consisting of two interconnected
more » ... el machines. MERAM technique is compared to Explicitly Restarted Arnoldi (ERAM) method, and one can notice that the accelaration of convergence is improved effectively. In some cases, more than one two-fold improvement can be seen in MERAM results. We also implemented MERAM on a cluster of workstations. According to our experiments, MERAM converges better than Explicitly Restarted Block Arnoldi method and, for some matrices, more quickly than PARPACK package which implements Implicitly Restarted Arnoldi Method.
doi:10.1137/s1064827500366082 fatcat:4b2o7rjcuzc5rfo5ih3jbouwhy