Interval arithmetic in cylindrical algebraic decomposition

Authors:
George E. Collins;Jeremy R. Johnson;Werner Krandick
Affiliations:
Computer and Information Sciences Department, University of Delaware, Newark, DE;Department of Mathematics and Computer Science, Drexel University, Philadelphia, PA;Department of Mathematics and Computer Science, Drexel University, Philadelphia, PA
Venue:
Journal of Symbolic Computation
Year:
2002

Citing 9
Cited 25

Partial Cylindrical Algebraic Decomposition for quantifier elimination

Journal of Symbolic Computation
Computing GCDs of polynomials over algebraic number fields

Journal of Symbolic Computation
Polynomial real root isolation using approximate arithmetic

ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Guaranteed solution formula construction

ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
On projection in CAD-based quantifier elimination with equational constraint

ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Multiprecision floating point addition

ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Interval arithmetic: From principles to implementation

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
Polynomial real root isolation using Descarte's rule of signs

SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation

QEPCAD B: a program for computing with semi-algebraic sets using CADs

ACM SIGSAM Bulletin
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
Real solution isolation using interval arithmetic

Computers & Mathematics with Applications
Complete numerical isolation of real zeros in zero-dimensional triangular systems

Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Fast and exact geometric analysis of real algebraic plane curves

Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Exact and efficient 2D-arrangements of arbitrary algebraic curves

Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Exact geometric-topological analysis of algebraic surfaces

Proceedings of the twenty-fourth annual symposium on Computational geometry
Developing a labelled object-relational constraint database architecture for the projection operator

Data & Knowledge Engineering
Complete numerical isolation of real roots in zero-dimensional triangular systems

Journal of Symbolic Computation
Univariate Algebraic Kernel and Application to Arrangements

SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
Lower bounds for zero-dimensional projections

Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Computing cylindrical algebraic decomposition via triangular decomposition

Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Isolating real roots of real polynomials

Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Experimental evaluation and cross-benchmarking of univariate real solvers

Proceedings of the 2009 conference on Symbolic numeric computation
An effective implementation of a symbolic-numeric cylindrical algebraic decomposition for quantifier elimination

Proceedings of the 2009 conference on Symbolic numeric computation
An efficient algorithm for the stratification and triangulation of an algebraic surface

Computational Geometry: Theory and Applications
A deterministic algorithm for isolating real roots of a real polynomial

Journal of Symbolic Computation
On solving systems of bivariate polynomials

ICMS'10 Proceedings of the Third international congress conference on Mathematical software
SqFreeEVAL: An (almost) optimal real-root isolation algorithm

Journal of Symbolic Computation
Differential dynamic logics: automated theorem proving for hybrid systems

Differential dynamic logics: automated theorem proving for hybrid systems
A descartes algorithm for polynomials with bit-stream coefficients

CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
An effective implementation of a symbolic-numeric cylindrical algebraic decomposition for optimization problems

Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
In Memoriam: Werner Krandick

ACM Communications in Computer Algebra
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
An effective implementation of symbolic-numeric cylindrical algebraic decomposition for quantifier elimination

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

Cylindrical algebraic decomposition requires many very time consuming operations, including resultant computation, polynomial factorization, algebraic polynomial gcd computation and polynomial real root isolation. We show how the time for algebraic polynomial real root isolation can be greatly reduced by using interval arithmetic instead of exact computation. This substantially reduces the overall time for cylindrical algebraic decomposition.