On the worst-case arithmetic complexity of approximating zeros of polynomials
Journal of Complexity
Simple algorithms for approximating all roots of a polynomial with real roots
Journal of Complexity
Mathematics for computer algebra
Mathematics for computer algebra
Parallel complexity of tridiagonal symmetric Eigenvalue problem
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Algorithms for polynomial real root isolation
Algorithms for polynomial real root isolation
A hybrid method for high precision calculation of polynomial real roots
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Complexity and real computation
Complexity and real computation
Computing Matrix Eigenvalues and Polynomial Zeros Where the Output is Real
SIAM Journal on Computing
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Univariate polynomials: nearly optimal algorithms for numerical factorization and root-finding
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Modern Computer Algebra
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Proceedings of the 2007 international workshop on Symbolic-numeric computation
On the asymptotic and practical complexity of solving bivariate systems over the reals
Journal of Symbolic Computation
On the topology of planar algebraic curves
Proceedings of the twenty-fifth annual symposium on Computational geometry
On the Complexity of Reliable Root Approximation
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Random polynomials and expected complexity of bisection methods for real solving
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
On solving systems of bivariate polynomials
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Theoretical Computer Science
Efficient real root approximation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Univariate real root isolation in an extension field
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Practical divide-and-conquer algorithms for polynomial arithmetic
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
ESA'05 Proceedings of the 13th annual European conference on Algorithms
A worst-case bound for topology computation of algebraic curves
Journal of Symbolic Computation
Long Integers and Polynomial Evaluation with Estrin's Scheme
SYNASC '11 Proceedings of the 2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
On the complexity of solving a bivariate polynomial system
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
When Newton meets Descartes: a simple and fast algorithm to isolate the real roots of a polynomial
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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We assume that a real square-free polynomial A has a degree d, a maximum coefficient bitsize τ and a real root lying in an isolating interval and having no nonreal roots nearby (we quantify this assumption). Then, we combine the Double Exponential Sieve algorithm (also called the Bisection of the Exponents), the bisection, and Newton iteration to decrease the width of this inclusion interval by a factor of t=2-L. The algorithm has Boolean complexity ÕB(d2 τ + d L ). Our algorithms support the same complexity bound for the refinement of r roots, for any r ≤ d.