Based on a model of a parallel vector computer with a shared memory, its scalability properties are derived. The processor-memory interconnection network is assumed to be composed of crossbar switches of size b/spl times/b. This paper analyzes sustainable peak performance under optimal conditions, i.e., no memory bank conflicts, sufficient processor-memory bank pathways, and no interconnection network conflicts. It will be shown that, with fully vectorizable algorithms and no communication overhead, the sustainable peak performance does not scale up linearly with the number of processors p. If the interconnection network is unbuffered, the number of memory banks must increase at least with O(p log/sub b/ p) to sustain peak performance. If the network is buffered, this bottleneck can be alleviated; however, the half performance vector length still increases with O(log/sub b/ p). The paper confirms the validity of the model by examining the performance behavior of the LINPACK benchmark.

Based on the parallel minimal norm method an algorithm is derived to solve tridiagonal linear systems with a high degree of parallelism. No conditions need to be posed with respect to the system. Experiments indicate that the numerical stability of the algorithm is similar to Gaussian elimination with partial pivoting.>