ACM Transactions on Mathematical Software 25 (2): 251–276. "Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation". "Homotop圜ontinuation.jl: A package for homotopy continuation in Julia". ↑ Breiding, Paul Timme, Sascha (May 2018).Mathematical software - ICMS 2014 : 4th International Congress, Seoul, South Korea, August 5-9, 2014. "Hom4PS-3: A Parallel Numerical Solver for Systems of Polynomial Equations Based on Polyhedral Homotopy Continuation Methods". ACM Transactions on Mathematical Software 38 (4): 1–20. "Algorithm 921: alphaCertified: Certifying Solutions to Polynomial Systems". Foundations of Computational Mathematics 13 (2): 253–295. The goal of this paper is to formulate spherical linkages analysis and design problems via a method suited to employ the tools of numerical algebraic geometry. "Robust Certified Numerical Homotopy Tracking" (in en). Numerical algebraic geometry is the field that studies the computation and manipulation of the solution sets of systems of polynomial equations. Communications in Information and Systems 15 (2): 276–277. "Homotopy continuation method for solving systems of nonlinear and polynomial equations" (in en). Society for Industrial and Applied Mathematics. Numerically solving polynomial systems with Bertini. Recently steps have been made to extend the reach of. Hauenstein, Jonathan D Wampler, Charles W. Numerical algebraic geometry SVW,SW is a relatively young subarea of compu-tational algebraic geometry that originated as a blend of the well-understood apparatus of classical algebraic geometry over the eld of complex numbers and numerical polynomial homotopy continua-tion methods. The numerical solution of systems of polynomials arising in engineering and science. Journal of Software for Algebra and Geometry 3 (1): 5–10. Solving polynomial equations : foundations, algorithms, and applications. "Introduction to Numerical Algebraic Geometry". Journal of Symbolic Computation 79: 499–507. Algebraic Geometry class notes by Andreas Gathmann. Macaulay2 (core implementation of homotopy tracking and NumericalAlgebraicGeometry package) Algebraic geometry: a first course by Joe Harris.Several software packages implement portions of the theoretical body of numerical algebraic geometry. This can be achieved in several ways, either a priori using a certified tracker, or a posteriori by showing that the point is, say, in the basin of convergence for Newton's method. Solutions to polynomial systems computed using numerical algebraic geometric methods can be certified, meaning that the approximate solution is "correct". This makes witness sets a good description of an algebraic variety. Thus, witness sets encode the answer to the first two questions one asks about an algebraic variety: What is the dimension, and what is the degree? Witness sets also allow one to perform a numerical irreducible decomposition, component membership tests, and component sampling. This is a specialization of the more general method of numerical continuation. The primary computational method used in numerical algebraic geometry is homotopy continuation, in which a homotopy is formed between two polynomial systems, and the isolated solutions (points) of one are continued to the other.
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