An improved upper complexity bound for the topology computation of a real algebraic plane curve
Journal of Complexity - Special issue for the Foundations of Computational Mathematics conference, Rio de Janeiro, Brazil, Jan. 1997
Fast algorithms for Taylor shifts and certain difference equations
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Asymptotically fast computation of subresultants
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Sylvester—Habicht sequences and fast Cauchy index computation
Journal of Symbolic Computation
Univariate polynomials: nearly optimal algorithms for numerical factorization and root-finding
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
A modular GCD algorithm over number fields presented with multiple extensions
Proceedings of the 2002 international symposium on Symbolic and algebraic 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
Root isolation for bivariate polynomial systems with local generic position method
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
An efficient algorithm for the stratification and triangulation of an algebraic surface
Computational Geometry: Theory and Applications
The DMM bound: multivariate (aggregate) separation bounds
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Efficient real root approximation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
A simple but exact and efficient algorithm for complex root isolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
A general approach to the analysis of controlled perturbation algorithms
Computational Geometry: Theory and Applications
A worst-case bound for topology computation of algebraic curves
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
Arrangement computation for planar algebraic curves
Proceedings of the 2011 International Workshop on Symbolic-Numeric 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
Rational univariate representations of bivariate systems and applications
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
From approximate factorization to root isolation
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
On the boolean complexity of real root refinement
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
On the complexity of solving bivariate systems: the case of non-singular solutions
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
| Hi-index | 0.00 |
We study the complexity of computing the real solutions of a bivariate polynomial system using the recently presented algorithm Bisolve [2]. Bisolve is an elimination method which, in a first step, projects the solutions of a system onto the x- and y-axes and, then, selects the actual solutions from the so induced candidate set. However, unlike similar algorithms, Bisolve requires no genericity assumption on the input, and there is no need for any kind of coordinate transformation. Furthermore, extensive benchmarks as presented in [2] confirm that the algorithm is highly practical, that is, a corresponding C++ implementation in Cgal outperforms state of the art approaches by a large factor. In this paper, we focus on the theoretical complexity of Bisolve. For two polynomials f, g ∈ Z[x, y] of total degree at most n with integer coefficients bounded by 2τ, we show that Bisolve computes isolating boxes for all real solutions of the system f = g = 0 using O(n8 + n7τ) bit operations, thereby improving the previous record bound for the same task by several magnitudes.