Challenge to fast and stable computation of approximate univariate GCD, based on displacement structures

Authors:
Masaru Sanuki
Affiliations:
University of Tsukuba, Tsukuba-Shi, Ibaraki, Japan
Venue:
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Year:
2012

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Abstract

Given polynomials with floating-point number coefficients, one can now compute the approximate GCD stably, except in ill-conditioned cases where the GCD has small or large leading coefficient/constant term. The cost is O(m2), where m is the maximum of degrees of given polynomials. On the other hand, for polynomial with integer coefficients, one can compute the polynomial GCD faster by using the half-GCD method with the cost less than O(m2). In this paper, we challenge to compute the approximate GCD faster, with the cost less than O(m2). Our idea is to use the displacement technique and the half-GCD method.