Issues raised in the implementation of dense linear algebra algorithms on a distributed memory architecture are discussed along with considerations that arise when the algorithms are implemented as general purpose library routines. We focus on a few methods which have proven to be important in the CMSSL implementation of elimination based algorithms such as LU and QR decomposition and bidiagonalization.

Selected Techniques for Efficient Parallel Implementation of Dense Linear Algebra Algorithms on the Connection Machine CM-5/CM/5E

The Singular Value Decomposition (SVD) is an algorithm that plays an essential role in many applications. There is a need for fast SVD algorithms in applications such as signal processing that require the SVD to be obtained or updated in real time. One technique for obtaining the SVD of a real dense matrix is to first reduce the dense matrix to bidiagonal form and then compute the SVD of the bidiagonal matrix. In this paper we describe how this approach can be implemented efficiently on the Connection Machine CM-5/CM-5E. Timing results show that use of the described techniques yields up to 45% of peak performance in the reduction from dense to bidiagonal form. Numerical results regarding the SVD computation of bidiagonal matrices illustrate that the approach considered yields accurate singular values as well as good performance. We also discuss the dependence between the accuracy of the singular values and the accuracy of the singular vectors.

Palle M. Pedersen

Papers

Singular Value Decomposition on the Connection Machine CM-5/CM-5E

Selected Techniques for Efficient Parallel Implementation of Dense Linear Algebra Algorithms on the Connection Machine CM-5/CM/5E