Gröbner bases and primary decomposition of polynomial ideals
Journal of Symbolic Computation
Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
Numerische Mathematik
Gröbner duality and multiplicities in polynomial system solving
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Numerical calculation of the multiplicity of a solution to algebraic equations
Mathematics of Computation
Involutive bases of polynomial ideals
Mathematics and Computers in Simulation - Special issue: Simplification of systems of algebraic and differential equations with applications
Solving projective complete intersection faster
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Multivariate polynomial system solving using intersections of Eigenspaces
Journal of Symbolic Computation
Gröbner-Bases, Gaussian elimination and resolution of systems of algebraic equations
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
A complete symbolic-numeric linear method for camera pose determination
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Numerical Polynomial Algebra
Computing the multiplicity structure in solving polynomial systems
Proceedings of the 2005 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
Newton's method with deflation for isolated singularities of polynomial systems
Theoretical Computer Science
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Numerical local rings and local solution of nonlinear systems
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Nearest multivariate system with given root multiplicities
Journal of Symbolic Computation
Deflation and certified isolation of singular zeros of polynomial systems
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
Computing the multiplicity structure of an isolated singular solution: Case of breadth one
Journal of Symbolic Computation
Numerical calculation of H-bases for positive dimensional varieties
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Computing Isolated Singular Solutions of Polynomial Systems: Case of Breadth One
SIAM Journal on Numerical Analysis
Verified error bounds for isolated singular solutions of polynomial systems: Case of breadth one
Theoretical Computer Science
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We present a method based on symbolic-numeric reduction to geometric involutive form to compute the primary component and the differential operators f solution of a polynomial ideal. The singular solution can be exact or approximate. If the singular solution is known with limited accuracy, then we propose a new method to refine it to high accuracy.