Andrew J. Sommese

Frank-Olaf Schreyer

Michael Eugene Stillman

SIAM J. Appl. Algebra Geom., 2019

2018

Polynomial Systems Arising From Discretizing Systems of Nonlinear Differential Equations.

[BibT_eX]

[DOI]

Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation, 2018

2017

Algorithm 976: Bertini_real: Numerical Decomposition of Real Algebraic Curves and Surfaces.

[BibT_eX]

[DOI]

ACM Trans. Math. Softw., 2017

Perturbation results on the zero-locus of a polynomial.

[BibT_eX]

[DOI]

Maria-Laura Torrente

Mauro Carlo Beltrametti

J. Symb. Comput., 2017

Homotopies for Connected Components of Algebraic Sets with Application to Computing Critical Sets.

[BibT_eX]

[DOI]

Proceedings of the Mathematical Aspects of Computer and Information Sciences, 2017

2015

Numerical Local Irreducible Decomposition.

[BibT_eX]

[DOI]

Proceedings of the Mathematical Aspects of Computer and Information Sciences, 2015

2014

A bootstrapping approach for computing multiple solutions of differential equations.

[BibT_eX]

[DOI]

J. Comput. Appl. Math., 2014

Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety.

[BibT_eX]

[DOI]

Wolfram Decker

Appl. Math. Comput., 2014

Bertini_real: Software for One- and Two-Dimensional Real Algebraic Sets.

[BibT_eX]

[DOI]

Proceedings of the Mathematical Software - ICMS 2014, 2014

On Computing a Cell Decomposition of a Real Surface Containing Infinitely Many Singularities.

[BibT_eX]

[DOI]

Proceedings of the Mathematical Software - ICMS 2014, 2014

2013

Algorithm 931: An algorithm and software for computing multiplicity structures at zeros of nonlinear systems.

[BibT_eX]

[DOI]

Zhonggang Zeng

ACM Trans. Math. Softw., 2013

Cell decomposition of almost smooth real algebraic surfaces.

[BibT_eX]

[DOI]

Gian Mario Besana

Sandra Di Rocco

Numer. Algorithms, 2013

Cell Cycle Control and Bifurcation for a Free Boundary Problem Modeling Tissue Growth.

[BibT_eX]

[DOI]

J. Sci. Comput., 2013

A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws.

[BibT_eX]

[DOI]

J. Comput. Phys., 2013

Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation.

[BibT_eX]

[DOI]

Timothy M. McCoy

J. Comput. Appl. Math., 2013

Recovering Exact Results from Inexact Numerical Data in Algebraic Geometry.

[BibT_eX]

[DOI]

Timothy M. McCoy

Chris Peterson

Exp. Math., 2013

Membership tests for images of algebraic sets by linear projections.

[BibT_eX]

[DOI]

Appl. Math. Comput., 2013

Numerically Solving Polynomial Systems with Bertini.

[BibT_eX]

[DOI]

Software, environments, tools 25, SIAM, ISBN: 978-1-611972-69-6, 2013

2012

Continuation Along Bifurcation Branches for a Tumor Model with a Necrotic Core.

[BibT_eX]

[DOI]

J. Sci. Comput., 2012

2011

Efficient path tracking methods.

[BibT_eX]

[DOI]

Numer. Algorithms, 2011

Regeneration homotopies for solving systems of polynomials.

[BibT_eX]

[DOI]

Math. Comput., 2011

Chern numbers of smooth varieties via homotopy continuation and intersection theory.

[BibT_eX]

[DOI]

J. Symb. Comput., 2011

Regenerative cascade homotopies for solving polynomial systems.

[BibT_eX]

[DOI]

Appl. Math. Comput., 2011

A three-dimensional steady-state tumor system.

[BibT_eX]

[DOI]

Appl. Math. Comput., 2011

Numerical algebraic geometry and algebraic kinematics.

[BibT_eX]

[DOI]

Acta Numer., 2011

2010

Algebraic C<sup>*</sup>-actions and the inverse kinematics of a general 6R manipulator.

[BibT_eX]

[DOI]

Appl. Math. Comput., 2010

Witness sets of projections.

[BibT_eX]

[DOI]

Appl. Math. Comput., 2010

2009

A Numerical Local Dimension Test for Points on the Solution Set of a System of Polynomial Equations.

[BibT_eX]

[DOI]

Chris Peterson

SIAM J. Numer. Anal., 2009

2008

Adaptive Multiprecision Path Tracking.

[BibT_eX]

[DOI]

SIAM J. Numer. Anal., 2008

Exceptional Sets and Fiber Products.

[BibT_eX]

[DOI]

Found. Comput. Math., 2008

2006

A numerical-symbolic algorithm for computing the multiplicity of a component of an algebraic set.

[BibT_eX]

[DOI]

Chris Peterson

J. Complex., 2006

Solution of Polynomial Systems Derived from Differential Equations.

[BibT_eX]

[DOI]

Computing, 2006

2005

An intrinsic homotopy for intersecting algebraic varieties.

[BibT_eX]

[DOI]

J. Complex., 2005

The numerical solution of systems of polynomials - arising in engineering and science.

[BibT_eX]

Charles W. Wampler II

World Scientific, ISBN: 978-981-256-184-8, 2005

2004

Numerical factorization of multivariate complex polynomials.

[BibT_eX]

[DOI]

Theor. Comput. Sci., 2004

Homotopies for Intersecting Solution Components of Polynomial Systems.

[BibT_eX]

[DOI]

SIAM J. Numer. Anal., 2004

2003

Numerical Irreducible Decomposition Using PHCpack.

[BibT_eX]

Proceedings of the Algebra, Geometry, and Software Systems [outcome of a Dagstuhl seminar], 2003

2002

Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems.

[BibT_eX]

[DOI]

SIAM J. Numer. Anal., 2002

Piecewise Linear Approximation of Smooth Compact Fibers.

[BibT_eX]

[DOI]

Eugene L. Allgower

J. Complex., 2002

2001

Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components.

[BibT_eX]

[DOI]

SIAM J. Numer. Anal., 2001

2000

Algorithm 801: POLSYS_PLP: a partitioned linear product homotopy code for solving polynomial systems of equations.

[BibT_eX]

[DOI]

Steven M. Wise

Layne T. Watson

ACM Trans. Math. Softw., 2000

Numerical Homotopies to Compute Generic Points on Positive Dimensional Algebraic Sets.

[BibT_eX]

[DOI]

J. Complex., 2000

1993

Ideals, Varieties, and Algorithms-An Introduction to Computational Algebraic Geometry and Commutative Algebra (D. Cox, J. Little, and D. O'Shea).

[BibT_eX]

[DOI]

SIAM Rev., 1993

1989

Finding all isolated solutions to polynomial systems using HOMPACK.

[BibT_eX]

[DOI]

Alexander P. Morgan