Title :
Specified precision polynomial root isolation is in NC
Author_Institution :
IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA
Abstract :
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-μ 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
Keywords :
computational complexity; parallel algorithms; polynomials; error; parallel complexity class NC; parallel time complexity; polynomial root isolation; precision; Arithmetic; Concurrent computing; Ear; Mathematics; Polynomials;
Conference_Titel :
Foundations of Computer Science, 1990. Proceedings., 31st Annual Symposium on
Conference_Location :
St. Louis, MO
Print_ISBN :
0-8186-2082-X
DOI :
10.1109/FSCS.1990.89534