Abstract

This paper presents a parallel implementation of a blocked band reduction algorithm for symmetric matrices suggested by Bischof and Sun. The reduction to tridiagonal or block tridiagonal form is a special case of this algorithm. A blocked double torus wrap mapping is used as the underlying data distribution and the so-called WY representation is employed to represent block orthogonal transformations. Preliminary performance results on the Intel Delta indicate that the algorithm is well-suited to a MIMD computing environment and that the use of a block approach significantly improves performance. 1 Introduction Reduction to tridiagonal form is a major step in eigenvalue computations for symmetric matrices. If the matrix is full, the conventional Householder tridiagonalization approach [13, p. 276] or block variants thereof [12] is the method of choice. These two approaches also underlie the parallel implementations described for example in [15] and [10]. The approach described in this ...

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