Mixed precision path tracking for polynomial homotopy continuation
From MaRDI portal
Publication:2240693
DOI10.1007/s10444-021-09899-yzbMath1487.65057arXiv1902.02968OpenAlexW3204208005MaRDI QIDQ2240693
Publication date: 4 November 2021
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1902.02968
Numerical computation of solutions to systems of equations (65H10) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20)
Related Items (5)
Landau discriminants ⋮ Contour Integration for Eigenvector Nonlinearities ⋮ Rigid continuation paths II. structured polynomial systems ⋮ Polyhedral homotopies in Cox coordinates ⋮ Locating the closest singularity in a polynomial homotopy
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Efficient path tracking methods
- On a problem posed by Steve Smale
- A unified derivation of several error bounds for Newton's process
- Coefficient-parameter polynomial continuation
- Numerical differentiation of implicitly defined space curves
- A stepsize control for continuation methods and its special application to multiple shooting techniques
- A power series method for computing singular solutions to nonlinear analytic systems
- HomotopyContinuation.jl: a package for homotopy continuation in Julia
- A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time
- Robust certified numerical homotopy tracking
- Computing singular solutions to nonlinear analytic systems
- Newton's Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems
- 3264 and All That
- Moment Varieties of Gaussian Mixtures
- Algorithm 921
- Smale’s 17th problem: Average polynomial time to compute affine and projective solutions
- Newton Methods for Nonlinear Problems
- Numerical algebraic geometry and algebraic kinematics
- Evaluating Derivatives
- Adaptive Multiprecision Path Tracking
- Higher Order Predictors and Adaptive Steplength Control in Path Following Algorithms
- Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
- An Interval Step Control for Continuation Methods
- Iterative refinement for linear systems and LAPACK
- A Fortran 90-based multiprecision system
- Algorithm 795
- Accuracy and Stability of Numerical Algorithms
- A continuation method based on a high order predictor and an adaptive steplength control
- Robust Padé Approximation via SVD
- A Robust Numerical Path Tracking Algorithm for Polynomial Homotopy Continuation
- 3264 Conics in a Second
- The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
This page was built for publication: Mixed precision path tracking for polynomial homotopy continuation
