Introduction to numerical algebraic geometry
@inproceedings{Sommese2005IntroductionTN, title={Introduction to numerical algebraic geometry}, author={Andrew J. Sommese and Jan Verschelde and Charles W. Wampler}, year={2005} }
In a 1996 paper, Andrew Sommese and Charles Wampler began developing a new area, “Numerical Algebraic Geometry”, which would bear the same relation to “Algebraic Geometry” that “Numerical Linear Algebra” bears to “Linear Algebra”.
68 Citations
Numerical Algebraic Geometry for Macaulay2
- Mathematics, Computer ScienceArXiv
- 2009
A package to interlink the existing symbolic methods of Macaulay2 and the powerful engine of numerical approximate computations to exhibit performance competitive with the other homotopy continuation software.
Computing Tropical Curves via Homotopy Continuation
- Computer Science, MathematicsExp. Math.
- 2016
This work exploits a connection between amoebas and tropical curves to devise a method for computing tropical curves using numerical algebraic geometry and gives an implementation that is used to compute Newton polygons of A-polynomials of knots.
Nonlinear algebra in 3 D computer vision
- Mathematics
- 2020
I study computational algebraic geometry—an amusing, somewhat more broad name for this field is nonlinear algebra. This field is firmly anchored to its algorithmic techniques—traditionally, symbolic…
General witness sets for numerical algebraic geometry
- MathematicsISSAC
- 2020
This work presents a general notion of witness set for subvarieties of a smooth complete complex algebraic variety using ideas from intersection theory, and introduces Schubert witness sets, which provide general witness sets for Grassmannians and flag manifolds.
Numerical algorithms for detecting embedded components
- Mathematics, Computer ScienceJ. Symb. Comput.
- 2017
Computing Puiseux series for algebraic surfaces
- Mathematics, Computer ScienceISSAC
- 2012
The preliminary methods produce exact representations for solution sets of the cyclic n-roots problem, for n = m2, corresponding to a result of Backelin.
Signatures of algebraic curves via numerical algebraic geometry
- Mathematics, Computer ScienceJournal of Symbolic Computation
- 2022
Galois groups of Schubert problems via homotopy computation
- MathematicsMath. Comput.
- 2009
This work shows by direct computation that the Galois group of the Schubert problem of 3-planes in ℂ 8 meeting 15 fixed 5-planes non-trivially is the full symmetric group S 6006.
Regularization and Matrix Computation in Numerical Polynomial Algebra
- Mathematics, Computer Science
- 2009
Regularization principles for reformulating the ill-posed algebraic problems, derive matrix computations arising in numerical polynomial algebra, as well as subspace strategies that substantially improve computational efficiency by reducing matrix sizes are developed.
References
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The numerical solution of systems of polynomials - arising in engineering and science
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Background: Polynomial Systems Homotopy Continuation Projective Spaces Probability One Polynomials of One Variable Other Methods Isolated Solutions: Coefficient-Parameter Homotopy Polynomial…
A geometric-numeric algorithm for absolute factorization of multivariate polynomials
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A new semi-numerical algorithmic method for factoring multivariate polynomials absolutely based on algebraic and geometric properties after reduction to the bivariate case in a generic system of coordinates is proposed.
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A semi-numerical algorithm for computing all irreducible branches of a curve in C3 defined by polynomials with rational coefficients is proposed, based on some properties appearing after a generic change of coordinate.