Andrew J. Sommese

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An intrinsic homotopy for intersecting algebraic varieties

Andrew J. Sommese, Jan Verschelde, Charles W. Wampler, 2005, J. Complex..

Collapsing the Resultant Dipole System

Layne T. Watson, Andrew J. Sommese, Alexander P. Morgan, 1987 .

Regeneration homotopies for solving systems of polynomials

Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler, 2010, Math. Comput..

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

Wenrui Hao, Andrew J. Sommese, Zhonggang Zeng, 2013, TOMS.

A Cascade Algorithm for Witness Supersets

Andrew J. Sommese, Charles W. Wampler, 2005 .

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

Andrew J. Sommese, Charles W. Wampler, C. Wampler, 2005 .

Algorithms in Algebraic Geometry (The IMA Volumes in Mathematics and its Applications)

Alicia Dickenstein, Andrew J. Sommese, Frank-Olaf Schreyer, 2007 .

Numerical algebraic geometry and algebraic kinematics

Andrew J. Sommese, Charles W. Wampler, C. Wampler, 2011, Acta Numerica.

Exceptional Sets and Fiber Products

Andrew J. Sommese, Charles W. Wampler, C. Wampler, 2008, Found. Comput. Math..

Numerically Solving Polynomial Systems with Bertini

Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler, 2013, Software, environments, tools.

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

Zhiliang Xu, Wenrui Hao, Chi-Wang Shu, 2013, J. Comput. Phys..

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

Wenrui Hao, Jonathan D. Hauenstein, Daniel A. Brake, 2014, ICMS.

Cell decomposition of almost smooth real algebraic surfaces

Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler, 2013, Numerical Algorithms.

Applying Numerical Algebraic Geometry to Kinematics

Andrew J. Sommese, Charles W. Wampler, C. Wampler, 2013 .

Numerical Homotopies to Compute Generic Points on Positive Dimensional Algebraic Sets

Andrew J. Sommese, Jan Verschelde, 2000, J. Complex..

Numerical factorization of multivariate complex polynomials

Andrew J. Sommese, Jan Verschelde, Charles W. Wampler, 2004, Theor. Comput. Sci..

Regenerative cascade homotopies for solving polynomial systems

Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler, 2011, Appl. Math. Comput..

Algebraic C*-actions and the inverse kinematics of a general 6R manipulator

Andrew J. Sommese, Charles W. Wampler, David Eklund, 2010, Appl. Math. Comput..

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

Yuan Liu, Wenrui Hao, Jonathan D. Hauenstein, 2012, Journal of Scientific Computing.

Polynomial Systems Arising From Discretizing Systems of Nonlinear Differential Equations

Andrew J. Sommese, 2018, ISSAC.

Adaptive Multiprecision Path Tracking

Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler, 2008, SIAM J. Numer. Anal..

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

Steven M. Wise, Layne T. Watson, Andrew J. Sommese, 2000, TOMS.

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

Jonathan D. Hauenstein, Daniel A. Brake, Andrew J. Sommese, 2014, ICMS.

Chern numbers of smooth varieties via homotopy continuation and intersection theory

Chris Peterson, Andrew J. Sommese, David Eklund, 2009, J. Symb. Comput..

Homotopies for Intersecting Solution Components of Polynomial Systems

Andrew J. Sommese, Jan Verschelde, Charles W. Wampler, 2004, SIAM J. Numer. Anal..

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

Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, 2013, J. Comput. Appl. Math..

Witness sets of projections

Jonathan D. Hauenstein, Andrew J. Sommese, J. Hauenstein, 2010, Appl. Math. Comput..

Solution of Polynomial Systems Derived from Differential Equations

Andrew J. Sommese, Charles W. Wampler, Eugene L. Allgower, 2005, Computing.

Singular Value Decomposition of Complexes

Jonathan D. Hauenstein, Daniel A. Brake, Andrew J. Sommese, 2018, SIAM J. Appl. Algebra Geom..

Efficient path tracking methods

Jonathan D. Hauenstein, Andrew J. Sommese, Daniel J. Bates, 2011, Numerical Algorithms.

Algorithm 976

Wenrui Hao, Jonathan D. Hauenstein, Daniel A. Brake, 2017, ACM Trans. Math. Softw..

A three-dimensional steady-state tumor system

Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, 2011, Appl. Math. Comput..

Checking Results and Other Implementation Tips

Andrew J. Sommese, Charles W. Wampler, 2005 .

Membership tests for images of algebraic sets by linear projections

Jonathan D. Hauenstein, Andrew J. Sommese, J. Hauenstein, 2013, Appl. Math. Comput..

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

Jonathan D. Hauenstein, Chris Peterson, Andrew J. Sommese, 2009, SIAM J. Numer. Anal..

A bootstrapping approach for computing multiple solutions of differential equations

Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, 2014, J. Comput. Appl. Math..

Software for numerical algebraic geometry: a paradigm and progress towards its implementation

Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler, 2008 .

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

Wenrui Hao, Andrew J. Sommese, Bei Hu, 2013, Journal of Scientific Computing.

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

Andrew J. Sommese, Jan Verschelde, Charles W. Wampler, 2000, SIAM J. Numer. Anal..

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

Chris Peterson, Andrew J. Sommese, Daniel J. Bates, 2006, J. Complex..

Piecewise Linear Approximation of Smooth Compact Fibers

Andrew J. Sommese, Eugene L. Allgower, 2002, J. Complex..

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

Jonathan D. Hauenstein, Chris Peterson, Andrew J. Sommese, 2014, Appl. Math. Comput..

Finding all isolated solutions to polynomial systems using HOMPACK

Layne T. Watson, Andrew J. Sommese, Alexander P. Morgan, 1989, TOMS.

Recovering Exact Results from Inexact Numerical Data in Algebraic Geometry

Jonathan D. Hauenstein, Chris Peterson, Andrew J. Sommese, 2013, Exp. Math..

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

Jonathan D. Hauenstein, Daniel A. Brake, Andrew J. Sommese, 2017, MACIS.

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

Andrew J. Sommese, 1993, SIAM Rev..

Numerical Local Irreducible Decomposition

Jonathan D. Hauenstein, Daniel A. Brake, Andrew J. Sommese, 2015, MACIS.

Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems

Andrew J. Sommese, Jan Verschelde, Charles W. Wampler, 2002, SIAM J. Numer. Anal..

Perturbation results on the zero-locus of a polynomial

Andrew J. Sommese, Mauro C. Beltrametti, Maria-Laura Torrente, 2017, J. Symb. Comput..

Numerical Irreducible Decomposition Using PHCpack

Andrew J. Sommese, Jan Verschelde, Charles W. Wampler, 2003, Algebra, Geometry, and Software Systems.