Solving tridiagonal systems of linear equations on the IBM 3090 VF
Tridiagonal systems of equations arise in the numerical solving of many problems in science and engineering which lead to models described by elliptic partial differential equations. The new trend in supercomputer architecture towards systems with a hierarchical memory structure coupled with vector and concurrent processing capabilities allow to exploit a high-level granularity of parallelism in algorithms. The paper under review deals with implementation of the Gaussian elimination and cyclic reduction on the parallel processor IBM 3900. This parallel system supports the efficiency of programming by efficient data transfer from the main memory to local memory and by minimizing the number of loads and stores from vector registers. For this machine, a modification LCR (local cyclic reduction) of the cyclic reduction algorithm is developed. Results of computational experiments, presented in the paper, show that the local variant of the cyclic reduction is superior to both the Gaussian elimination and original cyclic reduction.
scientific article; zbMATH DE number 4076450