Regenerative cascade homotopies for solving polynomial systems

DOI10.1016/j.amc.2011.06.004zbMath1231.65190OpenAlexW2093314258MaRDI QIDQ648311

Charles W. Wampler, Jonathan D. Hauenstein, Andrew John Sommese

Publication date: 22 November 2011

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2011.06.004

zbMATH Keywords

homotopy continuationpolynomial systemalgebraic setnumerical algebraic geometrycascade homotopynumerical irreducible decompositiongeneric pointswitness superset

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items (20)

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Uses Software

• Bertini
• POLSYS_GLP

Cites Work

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• Modified deflation algorithm for the solution of singular problems. I. A system of nonlinear algebraic equations
• Deflation algorithm for the multiple roots of a system of nonlinear equations
• Efficient path tracking methods
• HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method
• Permanental ideals
• Numerical homotopies to compute generic points on positive dimensional algebraic sets
• Newton's method with deflation for isolated singularities of polynomial systems
• Regeneration homotopies for solving systems of polynomials
• Algorithm 857
• Adaptive Multiprecision Path Tracking
• Algorithm 795
• Homotopies for Intersecting Solution Components of Polynomial Systems
• A Polyhedral Method for Solving Sparse Polynomial Systems
• Toward a Salmon Conjecture
• Computing the multiplicity structure in solving polynomial systems
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science

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