Abstract
Cyclic reduction, originally proposed by Hockney and Golub, is the most popular algorithm for solving tridiagonal linear systems on SIMD-type computers like CRAY-1 or CDC CYBER 205. That algorithm seems to be the adequate one for the IBM 3090 VF (uni-processor), too, although the overall expected speedup over Gaussian elimination, specialized for tridiagonal systems, is not as high as for the CRAY-1 or the CYBER 205. That is because the excellent scalar speed of the IBM 3090 makes its vector-to-scalar speed ratio relatively moderate. The idea of the cyclic reduction algorithm can be generalized and modified in various directions. A polyalgorithm can be derived which takes into account much better the given architecture of the IBM 3090 VF than the ‘pure’ cyclic reduction algorithm as described for instance by Kershaw. This is mainly achieved by introducing more locality into the formulae. For large systems of equations the well-known cache problems are prevented.
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