A highly parallel algorithm for root extraction

Journal Article · Wed Mar 01 04:00:00 EST 1989 · IEEE Trans. Comput.; (United States)

DOI:https://doi.org/10.1109/12.21130· OSTI ID:6275865

Rice, T A; Jamieson, L H

A new parallel algorithm for extracting the roots of a polynomial is presented. The algorithm is based on Graeffe's method, which is rarely used in serial implementations because it is slower than many common serial algorithms. However, Graeffe's method is particularly well suited to parallel implementation. Like many root finding algorithms, Graeffe's method is an iterative technique. Parallelism is used to reduce the execution time per iteration. The algorithm can employ a high degree of parallelism, and it requires only simple interprocessor communication. For a degree of n polynomial executed on an n + 1 processor SIMD machine, each iteration in the parallel algorithm has arithmetic complexity of approximately 2n and a communications overhead n. In general, arithmetic speedup is on the order of p/2 for a p-processor implementation.

• Research Organization: HP Signal Analysis Div., Rohnert Park, CA (US); School of Electrical Engineering, Purdue Univ., West Lafayette, IN (US)
• OSTI ID: 6275865
• Journal Information: IEEE Trans. Comput.; (United States), Journal Name: IEEE Trans. Comput.; (United States) Vol. 38:3; ISSN ITCOB
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990210* -- Supercomputers-- (1987-1989)
ALGORITHMS
ARRAY PROCESSORS
CALCULATION METHODS
COMMUNICATIONS
FUNCTIONS
ITERATIVE METHODS
MATHEMATICAL LOGIC
PARALLEL PROCESSING
POLYNOMIALS
PROGRAMMING