Fast algorithms for Taylor shifts and certain difference equations
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Polynomial real root isolation using approximate arithmetic
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Interval arithmetic in cylindrical algebraic decomposition
Journal of Symbolic Computation
Univariate polynomials: nearly optimal algorithms for numerical factorization and root-finding
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Polynomial real root isolation using Descarte's rule of signs
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Efficient isolation of polynomial's real roots
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Almost tight recursion tree bounds for the Descartes method
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Fast and exact geometric analysis of real algebraic plane curves
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
On the complexity of real root isolation using continued fractions
Theoretical Computer Science
Exact geometric-topological analysis of algebraic surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Complexity of real root isolation using continued fractions
Theoretical Computer Science
Experimental evaluation and cross-benchmarking of univariate real solvers
Proceedings of the 2009 conference on Symbolic numeric computation
New bounds for the Descartes method
Journal of Symbolic Computation
Faster algorithms for computing Hong's bound on absolute positiveness
Journal of Symbolic Computation
A descartes algorithm for polynomials with bit-stream coefficients
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Univariate real root isolation in an extension field
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Univariate real root isolation in multiple extension fields
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Improved bounds for the CF algorithm
Theoretical Computer Science
From approximate factorization to root isolation
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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We describe a bisection algorithm for root isolation of polynomials with real coefficients. It is assumed that the coefficients can be approximated with arbitrary precision; exact computation in the field of coefficients is not required. We refer to such coefficients as bitstream coefficients. The algorithm is simpler, deterministic and has better asymptotic complexity than the randomized algorithm of Eigenwillig et al. (2005). We also discuss a partial extension to multiple roots.