Gröbner bases and primary decomposition of polynomial ideals
Journal of Symbolic Computation
Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
Numerische Mathematik
A Gro¨bner approach to involutive bases
Journal of Symbolic Computation
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
A complete symbolic-numeric linear method for camera pose determination
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Computing the multiplicity structure in solving polynomial systems
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
Numerical local rings and local solution of nonlinear systems
Proceedings of the 2007 international workshop on Symbolic-numeric computation
A pommaret division algorithm for computing Grobner bases in boolean rings
Proceedings of the twenty-first 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
Solving polynomial systems via symbolic-numeric reduction to geometric involutive form
Journal of Symbolic Computation
Computing Isolated Singular Solutions of Polynomial Systems: Case of Breadth One
SIAM Journal on Numerical Analysis
Approximately singular systems and ill-conditioned polynomial systems
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Verified error bounds for isolated singular solutions of polynomial systems: Case of breadth one
Theoretical Computer Science
Finding points on real solution components and applications to differential polynomial systems
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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We present a method based on symbolic-numeric reduction to geometric involutive form to compute the primary component of and a basis of Max Noether space for a polynomial system at an isolated singular solution. The singular solution can be known exactly or approximately. For the case where the singular solution is known with limited accuracy, we then propose a generalized quadratic Newton iteration for refining it to high accuracy.