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A fast parallel algorithm for determining all roots of a polynomial with real roots

Journal Article · · SIAM J. Comput.; (United States)
DOI:https://doi.org/10.1137/0217069· OSTI ID:6390404

Given a polynomial rho(z) of degree n with m bit integer coefficients and an integer ..mu.., the problem of determining all its roots with error less than 2/sup -..mu../ is considered. It is shown that this problem is in the class NC if rho(z) has all real roots. Some very interesting properties of a Sturm sequence of a polynomial with distinct real roots are proved and used in the design of a fast parallel algorithm for this problem. Using Newton identities and a novel numerical integration scheme for evaluating a contour integral to high precision, this algorithm determines good approximations to the linear factors of rho(z).

Research Organization:
Hebrew Univ., Jerusalem (IL); IBM Thomas J. Watson Research Center, Yorktown Heights, NY (US); Dept. of Computer Science, Cornell Univ., Ithaca, NY (US); IBM Thomas J. Watson Research Center, Yorktown Heights, NY (US)
OSTI ID:
6390404
Journal Information:
SIAM J. Comput.; (United States), Journal Name: SIAM J. Comput.; (United States) Vol. 17:6; ISSN SMJCA
Country of Publication:
United States
Language:
English