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An efficient algorithm for infallible polynomial complex root isolation
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
A bibliography on roots of polynomials
Journal of Computational and Applied Mathematics
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Asymptotically fast computation of subresultants
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
New techniques for approximating complex polynomial zeros
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A Global Bisection Algorithm for Computing the Zeros of Polynomials in the Complex Plane
Journal of the ACM (JACM)
Fundamental problems of algorithmic algebra
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An Exact Method for Finding the Roots of a Complex Polynomial
ACM Transactions on Mathematical Software (TOMS)
Sylvester—Habicht sequences and fast Cauchy index computation
Journal of Symbolic Computation
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IEEE Computer Graphics and Applications
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
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Modular Algorithms In Symbolic Summation And Symbolic Integration (Lecture Notes in Computer Science)
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Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Almost tight recursion tree bounds for the Descartes method
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
On the complexity of real root isolation using continued fractions
Theoretical Computer Science
Complete subdivision algorithms, II: isotopic meshing of singular algebraic curves
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Complexity of real root isolation using continued fractions
Theoretical Computer Science
Proceedings of the twenty-fifth annual symposium on Computational geometry
Isolating real roots of real polynomials
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
New bounds for the Descartes method
Journal of Symbolic Computation
The design of core 2: a library for exact numeric computation in geometry and algebra
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
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Computational Geometry: Theory and Applications
SqFreeEVAL: An (almost) optimal real-root isolation algorithm
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
A general approach to the analysis of controlled perturbation algorithms
Computational Geometry: Theory and Applications
SqFreeEVAL: An (almost) optimal real-root isolation algorithm
Journal of Symbolic Computation
Empirical study of an evaluation-based subdivision algorithm for complex root isolation
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Non-local isotopic approximation of nonsingular surfaces
Computer-Aided Design
Local generic position for root isolation of zero-dimensional triangular polynomial systems
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Real and complex polynomial root-finding by means of eigen-solving
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
A root isolation algorithm for sparse univariate polynomials
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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
Near optimal tree size bounds on a simple real root isolation algorithm
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
On soft predicates in subdivision motion planning
Proceedings of the twenty-ninth annual symposium on Computational geometry
From approximate factorization to root isolation
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Finding the number of roots of a polynomial in a plane region using the winding number
Computers & Mathematics with Applications
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We present a new exact subdivision algorithm CEVAL for isolating the complex roots of a square-free polynomial in any given box. It is a generalization of a previous real root isolation algorithm called EVAL. Under suitable conditions, our approach is applicable for general analytic functions. CEVAL is based on the simple Bolzano Principle and is easy to implement exactly. Preliminary experiments have shown its competitiveness. We further show that, for the "benchmark problem" of isolating all roots of a square-free polynomial with integer coefficients, the asymptotic complexity of both algorithms EVAL and CEVAL matches (up a logarithmic term) that of more sophisticated real root isolation methods which are based on Descartes' Rule of Signs, Continued Fraction or Sturm sequence. In particular, we show that the tree size of EVAL matches that of other algorithms. Our analysis is based on a novel technique called Δ-clusters from which we expect to see further applications.