A parallel computational kernel for sparse nonsymmetric eigenvalue problems on multicomputers

The aim of this paper is to show an effective reorganization of the nonsymmetric block lanczos algorithm efficient, portable and scalable for multiple instructions multiple data (MIMD) distributed memory message passing architectures. Basic operations implemented here are matrix-matrix multiplications, eventually with a transposed and a sparse factor, LU factorisation and triangular systems solution. Since the communication overhead of the algorithm inhibits an efficient parallel implementation, we propose a reorganization of the block algorithm which reduces the total amount of communication involved in linear algebra operations. Then, we develop an efficient parallelization of the matrix-matrix multiplication when one of the factor is sparse. Some other linear algebra operations are performed using ScaLAPACK library. The parallel eigensolver has been tested on a cluster of PCs. All reported results show the proposed algorithm is efficient and scalable on the target architectures for problems of adequate dimension, and it can be the computational kernel of a robust software for large sparse eigenvalue problems.