Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Comparison of various multivariate resultant formulations
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Matrix computations (3rd ed.)
FOXBOX: a system for manipulating symbolic objects in black box representation
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Controlled iterative methods for solving polynomial systems
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Computing the isolated roots by matrix methods
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Symbolic computation in Java: an appraisement
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Matrices in elimination theory
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination
SIAM Journal on Matrix Analysis and Applications
Multivariate polynomials, duality, and structured matrices
Journal of Complexity
A Gröbner free alternative for polynomial system solving
Journal of Complexity
The STL Tutorial and Reference Guide: C++ Programming with the Standard Template Library
The STL Tutorial and Reference Guide: C++ Programming with the Standard Template Library
Systems of Algebraic Equations Solved by Means of Endomorphisms
AAECC-10 Proceedings of the 10th 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
LAPACK Working Note 20: A Portable Linear Algebra Library For High-Performance Computers
LAPACK Working Note 20: A Portable Linear Algebra Library For High-Performance Computers
A multivariate Weierstrass iterative rootfinder
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Relations between roots and coefficients, interpolation and application to system solving
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
A complete symbolic-numeric linear method for camera pose determination
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Generalized normal forms and polynomial system solving
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
On the complexity of real solving bivariate systems
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Computing the multiplicity structure from geometric involutive form
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Stable normal forms for polynomial system solving
Theoretical Computer Science
Solving polynomial systems via symbolic-numeric reduction to geometric involutive form
Journal of Symbolic Computation
On the asymptotic and practical complexity of solving bivariate systems over the reals
Journal of Symbolic Computation
Hybrid method for solving new pose estimation equation system
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
Resultant-based methods for plane curves intersection problems
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
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In this paper, we present a new method for solving square polynomial systems with no zero at infinity. We analyze its complexity, which indicates substantial improvements, compared with the previously known methods for solving such systems. We describe a framework for symbolic and numeric computations, developed in C++, in which we have implemented this algorithm. We mention the techniques that are involved in order to build efficient codes and compare with existing softwares. We end by some applications of this method, considering in particular an autocalibration problem in Computer Vision and an identification problem in Signal Processing, and report on the results of our first implementation.