Abstract

In this paper, we present an algorithm for the reduction to block upper-Hessenberg form which can be used to solve the nonsymmetric eigenvalue problem on message-passing multicomputers. On such multicomputers, a nonsymmetric matrix can be distributed across processing nodes con gured into a network of two-dimensional mesh processor array using a block-scattered decomposition. Based on the matrix partitioning and mapping, the algorithm employs both Householder re ectors and Givens rotations within each reduction step. We analyze the arithmetic and communication complexities and describe the implementation details of the algorithm on message-passing multicomputers. We discuss two di erent implementations|synchronous and asynchronous|and present performance results on the Intel iPSC/860 and DELTA. We conclude with an evaluation of the algorithm's communication cost, and suggest areas for further improvement. 1

Citations