The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The Organization of Computations for Uniform Recurrence Equations
Journal of the ACM (JACM)
An Efficient Parallel Algorithm for the Solution of a Tridiagonal Linear System of Equations
Journal of the ACM (JACM)
On the Parallel Evaluation of Polynomials
IEEE Transactions on Computers
Optimal algorithms for parallel polynomial evaluation
Journal of Computer and System Sciences
The complexity of parallel evaluation of linear recurrence
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
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This paper presents new algorithms for the parallel evaluation of certain polynomial expression. In particular, for the parallel evaluation of xn,we introduce an algorithm which takes two steps of parallel division and [log2n] steps of parallel addition, while the usual algorithm takes [log2n] steps of parallel multiplication. Hence our algorithm is faster than the usual algorithms when multiplication takes more time than addition. Similar algorithm for the evaluation of other polynomial expressions are also introduced. Lower bounds on the time needed for the parallel evaluation of rational expressions are given. All the algorithms presented in the paper are shown to be asymptotically optimal. Moreover, we prove that by using parallelism the evaluation of any first order rational recurrence, e.g., [equation], and any non-linear polynomial recurrence can be sped up at most by a constant factor, no matter how many processors are used.