Using monodromy to avoid high precision in homotopy continuation

DOI10.1007/s11786-014-0190-0zbMath1302.65137OpenAlexW2123718967MaRDI QIDQ475409

Daniel J. Bates, Matthew E. Niemerg

Publication date: 27 November 2014

Published in: Mathematics in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11786-014-0190-0

Mathematics Subject Classification ID

Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Solving polynomial systems; resultants (13P15)

Uses Software

• HOM4PS
• Macaulay2
• PHCpack
• Bertini
• alphaCertified
• Paramotopy
• NAG4M2
• NumericalAlgebraicGeometry

Cites Work

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• Sweeping algebraic curves for singular solutions
• HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method
• Paramotopy: parameter homotopies in parallel
• Robust certified numerical homotopy tracking
• Numerical algebraic geometry
• Solving nonlinear equations by adaptive homotopy continuation
• Computing singular solutions to nonlinear analytic systems
• Algorithm 921
• Galois groups of Schubert problems via homotopy computation
• Regeneration homotopies for solving systems of polynomials
• Adaptive Multiprecision Path Tracking
• An Interval Step Control for Continuation Methods
• Algorithm 795
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
• Certified Parallelotope Continuation for One-Manifolds

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