The complexity of robot motion planning
The complexity of robot motion planning
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Solving systems of nonlinear polynomial equations faster
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Kinematic analysis of the 6R manipulator of general geometry
The fifth international symposium on Robotics research
LAPACK's user's guide
Solving zero-dimensional algebraic systems
Journal of Symbolic Computation
Multipolynomial resultant algorithms
Journal of Symbolic Computation
Algebraic and numeric techniques in modeling and robotics
Algebraic and numeric techniques in modeling and robotics
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
Journal of Symbolic Computation
Introduction to Robotics: Mechanics and Control
Introduction to Robotics: Mechanics and Control
Solving Systems of Polynomial Equations
IEEE Computer Graphics and Applications
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
An Efficient Algorithm for the Sparse Mixed Resultant
AAECC-10 Proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Numeric-symbolic algorithms for evaluating one-dimensional algebraic sets
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
An efficient surface intersection algorithm based on lower-dimensional formulation
ACM Transactions on Graphics (TOG)
Solving algebraic systems using matrix computations
ACM SIGSAM Bulletin
Controlled iterative methods for solving polynomial systems
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Efficient And Accurate Interference Detection For Polynomial Deformation
CA '96 Proceedings of the Computer Animation
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We present efficient and accurate algorithms to compute solutions of zero-dimensional multivariate polynomial equations in a given domain. Earlier methods for solving polynomial equations are based on iterative methods, homotopy methods or symbolic elimination. The total number of solutions correspond to the Bezout bound for dense polynomial systems or the BKK bound for sparse systems. In most applications the actual number of solutions in the domain of interest is much lower than the Bezout or BKK bound. Our approach is based on global formulation of the problem using resultants and matrix computations and localizing it to find selected solutions only. The problem of finding roots is reduced to computing eigenvalues of a generalized companion matrix and we use the structure of the matrix to compute the solutions in the domain of interest only. The resulting algorithm is iterative in nature and we discuss its performance on a number of applications.