A Robust Numerical Path Tracking Algorithm for Polynomial Homotopy Continuation
DOI10.1137/19M1288036zbMath1457.65023arXiv1909.04984MaRDI QIDQ5146689
Jan Verschelde, Simon Telen, Marc Van Barel
Publication date: 26 January 2021
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1909.04984
homotopy continuationpower seriespolynomial systemsPadé approximanta priori stepsize controlFabry ratio theorem
Numerical computation of solutions to systems of equations (65H10) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Padé approximation (41A21) Numerical computation of roots of polynomial equations (65H04)
Related Items (9)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- An algorithm for computing a Padé approximant with minimal degree denominator
- Sweeping algebraic curves for singular solutions
- Deformation techniques for sparse systems
- Puiseux expansion for space curves
- A power series method for computing singular solutions to nonlinear analytic systems
- Polyhedral end games for polynomial continuation
- Symmetric homotopy construction
- The convergence of Padé approximants to functions with branch points
- A stabilized normal form algorithm for generic systems of polynomial equations
- HomotopyContinuation.jl: a package for homotopy continuation in Julia
- Robust certified numerical homotopy tracking
- The method of Gauss-Newton to compute power series solutions of polynomial homotopies
- Algebraic properties of robust Padé approximants
- On the location of poles of Padé approximants
- Computing singular solutions to nonlinear analytic systems
- Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components
- Condition
- THE POLES OF THEmTH ROW OF THE PADÉ TABLE AND THE SINGULAR POINTS OF A FUNCTION
- Evaluating Derivatives
- Adaptive Multiprecision Path Tracking
- Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems
- ON AN INVERSE PROBLEM FOR THEmTH ROW OF THE PADÉ TABLE
- Higher Order Predictors and Adaptive Steplength Control in Path Following Algorithms
- Automatic Hessians by reverse accumulation
- ON THE CONVERGENCE OF GENERALIZED PADÉ APPROXIMANTS OF MEROMORPHIC FUNCTIONS
- Fast Algorithms for Manipulating Formal Power Series
- An Interval Step Control for Continuation Methods
- Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems
- Introduction to Numerical Continuation Methods
- Padé approximants and efficient analytic continuation of a power series
- Algorithm 795
- A Neural Network Modeled by an Adaptive Lotka-Volterra System
- A continuation method based on a high order predictor and an adaptive steplength control
- A Polyhedral Method for Solving Sparse Polynomial Systems
- Robust Padé Approximation via SVD
- The Holomorphic Embedding Loadflow Method for DC Power Systems and Nonlinear DC Circuits
- An Approach for Certifying Homotopy Continuation Paths
- Fast and Backward Stable Computation of Roots of Polynomials
- The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
- The AAA Algorithm for Rational Approximation
This page was built for publication: A Robust Numerical Path Tracking Algorithm for Polynomial Homotopy Continuation
