Efficient Eigenvalue Computation of Symmetric Tridiagonal Matrices on Heterogeneous Workstation Clusters

Abstract

Many computation-intensive problems require costly platforms such as supercomputers or massively parallel computers (MPC) in order to achieve reasonable execution speed. Recently, due to the popularity of workstation and computer network, workstation clusters emerge as a low-cost alternative of parallel and distributed computing for applications requiring large amount of computations. This paper utilizes heterogeneous workstation clusters composed of various types of machines to calculate the eigenvaluse of symmeyric tridiagonal matrices, a problem frequently encountered in many scientific and engineering applications. Among the parallel algorithms for eigenvalue problems, the split-and-merge method with Laguerre's iteration is selected due to its inherent high parallelism, low communication overhead and suitability for distributed implementation. The computation platform consists of clusters of non-dedicated workstations connected by Ethernet with PVM (Parallel Virtual Machine) as the supporting software package. Various heterogeneous configurations are tested and compared to find a best machine combination given a fixed overall normalized computing power. To improve the computation efficiency, both static and dynamic load balancing is considered especially when the multi-user environment has highly uneven and timechanging load. The experimental data shows promising results of significant speed-up compared to the sequential implementations.