关键词：算法；通信；对称矩阵；并行算法
摘 要：The running time of an algorithm depends on both arithmetic and communication (i.e., data movement) costs, and the relative costs of communication are growing over time. In this work, we present sequential and parallel algorithms for tridiagonalizing a symmetric band matrix that asymptotically reduce communication compared to previous approaches. The tridiagonalization of a symmetric band matrix is a key kernel in solving the symmetric eigenvalue problem for both full and band matrices. In order to preserve sparsity, tridiagonalization routines use annihilate-and-chase procedures that previously have su ered from poor data locality. We improve data locality by reorganizing the computation and obtain asymptotic improvements. We consider the cases of computing eigenvalues only and of computing eigenvalues and all eigenvectors.