A Generalized Criterion For The Early Termination Of R-Cyclic Reduction And Divide-And-Conquer For Recurrences

In this paper we deal with the parallel solution of linear recurrences x{sub i} = b{sub i}+a{sub i} x{sub i-1} for the case {vert_bar}a{sub i}{vert_bar} u003c 1. Criteria for saving arithmetic operations to the R-Cyclic Reduction and the Divide and Conquer families of parallel algorithms are proposed. Expressions are obtained that indicate the phase in which the algorithms have to be terminated as a function of the maximum absolute value of jail and the maximum absolute error allowed to the solution. Also, an analysis of the most important features of these two algorithms when terminated early is performed. Execution times of both algorithms for general and Teoplitz systems are given on one vector processor of the Convex C-3480.