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Recent progress in polynomial elimination has rendered the computation of the real roots of ill-conditioned polynomials of high degree (over 1000) with huge coefficients (several thousand digits) a critical operation in computer algebra. To rise to the occasion, the only method-candidate that has been considered by various authors for modification and improvement has been the Collins-Akritas bisection method , which is a based on a variation of Vincent's theorem . The most recent exampledoi:10.15388/na.2005.10.4.15110 fatcat:b2npwsohefes3pufdlpylwudpm