Parallel arithmetic computations: a survey
Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Differential equations and dynamical systems
Differential equations and dynamical systems
Mathematics for computer algebra
Mathematics for computer algebra
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Homotopies exploiting Newton polytopes for solving sparse polynomial systems
SIAM Journal on Numerical Analysis
Basic algebraic geometry 1 (2nd, revised and expanded ed.)
Basic algebraic geometry 1 (2nd, revised and expanded ed.)
A product-decomposition bound for Bezout numbers
SIAM Journal on Numerical Analysis
A polyhedral method for solving sparse polynomial systems
Mathematics of Computation
On the efficiency of effective Nullstellensa¨tze
Computational Complexity
Moving Mesh Methods for Problems with Blow-up
SIAM Journal on Scientific Computing
Complexity and real computation
Complexity and real computation
Blowup in diffusion equations: a survey
Journal of Computational and Applied Mathematics - Special issue: nonlinear problems with blow-up solutions: applications and numerical analysis
Modern computer algebra
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Deformation techniques for efficient polynomial equation solving
Journal of Complexity
Sylvester—Habicht sequences and fast Cauchy index computation
Journal of Symbolic Computation
A Gröbner free alternative for polynomial system solving
Journal of Complexity
Models of Computation: Exploring the Power of Computing
Models of Computation: Exploring the Power of Computing
Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components
SIAM Journal on Numerical Analysis
Polynomial equation solving by lifting procedures for ramified fibers
Theoretical Computer Science - Algebraic and numerical algorithm
Deformation techniques to solve generalised Pham systems
Theoretical Computer Science - Algebraic and numerical algorithm
Approximation of the solution of certain nonlinear ODEs with linear complexity
Journal of Computational and Applied Mathematics
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We consider a family of polynomial systems which arises in the analysis of the stationary solutions of a standard discretization of certain semi-linear second-order parabolic partial differential equations. We prove that this family is well-conditioned from the numeric point of view, and ill-conditioned from the symbolic point of view. We exhibit a polynomial-time numeric algorithm solving any member of this family, which significantly contrasts the exponential behavior of all known symbolic algorithms solving a generic instance of this family of systems.