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Specified precision polynomial root isolation is in NC

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1 Author(s)
Neff, C.A. ; IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA

Given a polynomial p(z) od degree n with integer coefficients, whose absolute values are bounded above by 2 m, and a specified integer μ, it is shown that the problem of determining all roots of p with error less than 2 is in the parallel complexity class NC. To do this, an algorithm that runs on at most POLY(n+m+μ) processors with a parallel time complexity of O(log3(n+m +μ)) is constructed. This algorithm extends the algorithm of M. Ben-Or et al. (SIAM J. Comput., vol.17, p.1081-92, 1988) by removing the severe restriction that all the roots of p(z) should be real

Published in:

Foundations of Computer Science, 1990. Proceedings., 31st Annual Symposium on

Date of Conference:

22-24 Oct 1990