Approximate square-free decomposition and root-finding of lll-conditioned algebraic equations
Journal of Information Processing
Approximate GCD and its application to ill-conditioned algebraic equations
ISCM '90 Proceedings of the International Symposium on Computation mathematics
Journal of Symbolic Computation
Journal of Information Processing
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
Polynomial root finding using iterated Eigenvalue computation
Proceedings of the 2001 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
Approximate radical of ideals with clusters of roots
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
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
A Theory and an Algorithm of Approximate Gröbner Bases
SYNASC '11 Proceedings of the 2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
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By "approximately singular system" we mean a system of multivariate polynomials the dimension of whose variety is increased by small amounts of perturbations. First, we give a necessary condition that the given system is approximately singular. Then, we classify polynomial systems which seems ill-conditioned to solve numerically into four types. Among these, the third one is approximately singular type. We give a simple well-conditioning method for the third type. We test the third type and its well-conditioned systems by various examples, from viewpoints of "global convergence", "local convergence" and detail of individual computation. The results of experiments show that our well-conditioning method improves the global convergence largely.