Quantifier elimination and the sign variation method for real root isolation
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Polynomial real root isolation using approximate arithmetic
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Parallel Real Root Isolation Using the Descartes Method
HiPC '99 Proceedings of the 6th International Conference on High Performance Computing
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
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
Compiler-enforced memory semantics in the SACLIB computer algebra library
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
New bounds for the Descartes method
ACM SIGSAM Bulletin
Almost tight recursion tree bounds for the Descartes method
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
High-performance implementations of the Descartes method
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Journal of Computational and Applied Mathematics
Univariate polynomial real root isolation: continued fractions revisited
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Fast and exact geometric analysis of real algebraic plane curves
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Complexity of real root isolation using continued fractions
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
On the complexity of real root isolation using continued fractions
Theoretical Computer Science
Real Algebraic Numbers: Complexity Analysis and Experimentation
Reliable Implementation of Real Number Algorithms: Theory and Practice
Complexity of real root isolation using continued fractions
Theoretical Computer Science
ACM Transactions on Graphics (TOG)
A deterministic algorithm for isolating real roots of a real polynomial
Journal of Symbolic Computation
Algebraic and numerical algorithms
Algorithms and theory of computation handbook
A simple but exact and efficient algorithm for complex root isolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
SqFreeEVAL: An (almost) optimal real-root isolation algorithm
Journal of Symbolic Computation
Compiler-enforced memory semantics in the SACLIB computer algebra library
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
On the computing time of the continued fractions method
Journal of Symbolic Computation
ACM Communications in Computer Algebra
Improved bounds for the CF algorithm
Theoretical Computer Science
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We give a new bound for the number of recursive subdivisions in the Descartes method for polynomial real root isolation. Our proof uses Ostrowski's theory of normal power series from 1950 which has so far been overlooked in the literature. We combine Ostrowski's results with a theorem of Davenport from 1985 to obtain our bound. We also characterize normality of cubic polynomials by explicit conditions on their roots and derive a generalization of one of Ostrowski's theorems.