Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
The consistent intialization of differential-algebraic systems
SIAM Journal on Scientific and Statistical Computing
Counting connected components of a semialgebraic set in subexponential time
Computational Complexity
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Improvements in cad-based quantifier elimination
Improvements in cad-based quantifier elimination
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Implicit Riquier Bases for PDAE and their semi-discretizations
Journal of Symbolic Computation
A prolongation-projection algorithm for computing the finite real variety of an ideal
Theoretical Computer Science
Computing cylindrical algebraic decomposition via triangular decomposition
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
Triangular decomposition of semi-algebraic systems
Journal of Symbolic Computation
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In this paper we extend complex homotopy methods to finding witness points on the irreducible components of real varieties. In particular we construct such witness points as the isolated real solutions of a constrained optimization problem. First a random hyperplane characterized by its random normal vector is chosen. Witness points are computed by a polyhedral homotopy method. Some of them are at the intersection of this hyperplane with the components. Other witness points are the local critical points of the distance from the plane to components. A method is also given for constructing regular witness points on components, when the critical points are singular. The method is applicable to systems satisfying certain regularity conditions. Illustrative examples are given. We show that the method can be used in the consistent initialization phase of a popular method due to Pryce and Pantelides for preprocessing differential algebraic equations for numerical solution.