A fast parallel algorithm for determining all roots of a polynomial with real roots
Journal Article
·
· SIAM J. Comput.; (United States)
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
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