The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Integer Arithmetic Algorithms for Polynomial Real Zero Determination
Journal of the ACM (JACM)
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
An algorithm for generalized point location and its applications
Journal of Symbolic Computation
Real zero isolation for trigonometric polynomials
ACM Transactions on Mathematical Software (TOMS)
Real algebraic number computation using interval arithmetic
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
An Algorithm for Deciding the Convergence of the Rational Iteration xn+1= f(xn)
ACM Transactions on Mathematical Software (TOMS)
A new method for polynomial real root isolation
ACM-SE 16 Proceedings of the 16th annual Southeast regional conference
On the sign of a real algebraic number
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Polynomial real root isolation using Descarte's rule of signs
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Real root isolation for algebraic polynomials
ACM SIGSAM Bulletin
Deciding polynomial-exponential problems
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
The polynomial roots repartition and minimum roots separation
WSEAS Transactions on Mathematics
Isolating the polynomial roots with all zeros real
ICCOMP'08 Proceedings of the 12th WSEAS international conference on Computers
Direct trimming of NURBS surfaces on the GPU
ACM SIGGRAPH 2009 papers
Cost reduction on roots pre-isolation
AIKED'09 Proceedings of the 8th WSEAS international conference on Artificial intelligence, knowledge engineering and data bases
Comparative methods for the polynomial isolation
ICCOMP'09 Proceedings of the WSEAES 13th international conference on Computers
Univariate real root isolation in an extension field
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Deciding polynomial-transcendental problems
Journal of Symbolic Computation
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A new algorithm is described, for the isolation of the real roots of a real polynomial. This algorithm utilizes the sequence of derivatives of the given polynomial, relying on Rolle's theorem and a tangent construction to decide whether an interval contains two roots or none. The algorithm is carefully compared, both analytically and empirically, with an algorithm based on Sturm's theorem, and is found to be significantly faster in general. It also requires less memory, and produces isolating intervals for the derivatives as a cost-free by-product.