Adaptive Multiprecision Path Tracking. - Daniel J. Bates; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (SIAM J. Numer. Anal., 2008)

A Numerical Local Dimension Test for Points on the Solution Set of a System of Polynomial Equations. - Daniel J. Bates; Jonathan D. Hauenstein; Chris Peterson 001; Andrew J. Sommese (SIAM J. Numer. Anal., 2009)

Witness sets of projections. - Jonathan D. Hauenstein; Andrew J. Sommese (Appl. Math. Comput., 2010)

alphaCertified: certifying solutions to polynomial systems - Jonathan D. Hauenstein; Frank Sottile (CoRR, 2010)

A three-dimensional steady-state tumor system. - Wenrui Hao; Jonathan D. Hauenstein; Bei Hu; Andrew J. Sommese (Appl. Math. Comput., 2011)

Regenerative cascade homotopies for solving polynomial systems. - Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (Appl. Math. Comput., 2011)

Regeneration homotopies for solving systems of polynomials. - Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (Math. Comput., 2011)

Efficient path tracking methods. - Daniel J. Bates; Jonathan D. Hauenstein; Andrew J. Sommese (Numer. Algorithms, 2011)

Continuation Along Bifurcation Branches for a Tumor Model with a Necrotic Core. - Wenrui Hao; Jonathan D. Hauenstein; Bei Hu; Yuan Liu 018; Andrew J. Sommese; Yong-Tao Zhang (J. Sci. Comput., 2012)

Algorithm 921: alphaCertified: Certifying Solutions to Polynomial Systems. - Jonathan D. Hauenstein; Frank Sottile (ACM Trans. Math. Softw., 2012)

Numerically Solving Polynomial Systems with Bertini. - Daniel J. Bates; Andrew J. Sommese; Jonathan D. Hauenstein; Charles W. Wampler (SIAM, 2013)

Membership tests for images of algebraic sets by linear projections. - Jonathan D. Hauenstein; Andrew J. Sommese (Appl. Math. Comput., 2013)

Numerically intersecting algebraic varieties via witness sets. - Jonathan D. Hauenstein; Charles W. Wampler (Appl. Math. Comput., 2013)

Computer aided methods for lower bounds on the border rank - Jonathan D. Hauenstein; Christian Ikenmeyer; J. M. Landsberg (CoRR, 2013)

Recovering Exact Results from Inexact Numerical Data in Algebraic Geometry. - Daniel J. Bates; Jonathan D. Hauenstein; Timothy M. McCoy; Chris Peterson 001; Andrew J. Sommese (Exp. Math., 2013)

Equations for Lower Bounds on Border Rank. - Jonathan D. Hauenstein; Christian Ikenmeyer; J. M. Landsberg (Exp. Math., 2013)

Isosingular Sets and Deflation. - Jonathan D. Hauenstein; Charles W. Wampler (Found. Comput. Math., 2013)

Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation. - Wenrui Hao; Jonathan D. Hauenstein; Bei Hu; Timothy M. McCoy; Andrew J. Sommese (J. Comput. Appl. Math., 2013)

A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws. - Wenrui Hao; Jonathan D. Hauenstein; Chi-Wang Shu; Andrew J. Sommese; Zhiliang Xu; Yong-Tao Zhang (J. Comput. Phys., 2013)

Cell decomposition of almost smooth real algebraic surfaces. - GianMario Besana; Sandra Di Rocco; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (Numer. Algorithms, 2013)

A Note on Global Newton Iteration Over Archimedean and Non-Archimedean Fields. - Jonathan D. Hauenstein; Victor Y. Pan; Ágnes Szántó (CASC, 2014)

On Computing a Cell Decomposition of a Real Surface Containing Infinitely Many Singularities. - Daniel J. Bates; Daniel A. Brake; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (ICMS, 2014)

Bertini_real: Software for One- and Two-Dimensional Real Algebraic Sets. - Daniel A. Brake; Daniel J. Bates; Wenrui Hao; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (ICMS, 2014)

An a posteriori certification algorithm for Newton homotopies. - Jonathan D. Hauenstein; Ian Haywood; Alan C. Liddell Jr. (ISSAC, 2014)

Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety. - Daniel J. Bates; Wolfram Decker; Jonathan D. Hauenstein; Chris Peterson 001; Gerhard Pfister; Frank-Olaf Schreyer; Andrew J. Sommese; Charles W. Wampler (Appl. Math. Comput., 2014)

Certified counting of roots of random univariate polynomials. - Joseph Cleveland; Jeffrey Dzugan; Jonathan D. Hauenstein; Ian Haywood; Dhagash Mehta; Anthony Morse; Leonardo Robol; Taylor Schlenk (CoRR, 2014)

Global Newton Iteration over Archimedean and non-Archimedean Fields. - Jonathan D. Hauenstein; Victor Y. Pan; Ágnes Szántó (CoRR, 2014)

A bootstrapping approach for computing multiple solutions of differential equations. - Wenrui Hao; Jonathan D. Hauenstein; Bei Hu; Andrew J. Sommese (J. Comput. Appl. Math., 2014)

Newton Polytopes and Witness Sets. - Jonathan D. Hauenstein; Frank Sottile (Math. Comput. Sci., 2014)

A hybrid symbolic-numeric approach to exceptional sets of generically zero-dimensional systems. - Jonathan D. Hauenstein; Alan C. Liddell Jr. (PASCO, 2015)

Certifying Isolated Singular Points and their Multiplicity Structure. - Jonathan D. Hauenstein; Bernard Mourrain; Ágnes Szántó (ISSAC, 2015)

Numerical Local Irreducible Decomposition. - Daniel A. Brake; Jonathan D. Hauenstein; Andrew J. Sommese (MACIS, 2015)

Numerically Testing Generically Reduced Projective Schemes for the Arithmetic Gorenstein Property. - Noah S. Daleo; Jonathan D. Hauenstein (MACIS, 2015)

Experiments on the Zeros of Harmonic Polynomials Using Certified Counting. - Jonathan D. Hauenstein; Antonio Lerario; Erik Lundberg; Dhagash Mehta (Exp. Math., 2015)

Decomposing Solution Sets of Polynomial Systems Using Derivatives. - Daniel A. Brake; Jonathan D. Hauenstein; Alan C. Liddell Jr. (ICMS, 2016)

Validating the Completeness of the Real Solution Set of a System of Polynomial Equations. - Daniel A. Brake; Jonathan D. Hauenstein; Alan C. Liddell Jr. (ISSAC, 2016)

Numerically validating the completeness of the real solution set of a system of polynomial equations. - Daniel A. Brake; Jonathan D. Hauenstein; Alan C. Liddell Jr. (CoRR, 2016)

Investigating the Maximum Number of Real Solutions to the Power Flow Equations: Analysis of Lossless Four-Bus Systems. - Daniel K. Molzahn; Matthew E. Niemerg; Dhagash Mehta; Jonathan D. Hauenstein (CoRR, 2016)

Complexity of Linear Circuits and Geometry. - Fulvio Gesmundo; Jonathan D. Hauenstein; Christian Ikenmeyer; J. M. Landsberg (Found. Comput. Math., 2016)

A Primal-Dual Formulation for Certifiable Computations in Schubert Calculus. - Jonathan D. Hauenstein; Nickolas Hein; Frank Sottile (Found. Comput. Math., 2016)

Numerically deciding the arithmetically Cohen-Macaulayness of a projective scheme. - Noah S. Daleo; Jonathan D. Hauenstein (J. Symb. Comput., 2016)

Certified predictor-corrector tracking for Newton homotopies. - Jonathan D. Hauenstein; Alan C. Liddell Jr. (J. Symb. Comput., 2016)

Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials. - Daniel J. Bates; Jonathan D. Hauenstein; Matthew E. Niemerg; Frank Sottile (Numer. Algorithms, 2016)

Homotopies for Connected Components of Algebraic Sets with Application to Computing Critical Sets. - Daniel J. Bates; Daniel A. Brake; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (MACIS, 2017)

Certification Using Newton-Invariant Subspaces. - Jonathan D. Hauenstein (MACIS, 2017)

Unification and extension of intersection algorithms in numerical algebraic geometry. - Jonathan D. Hauenstein; Charles W. Wampler (Appl. Math. Comput., 2017)

On deflation and multiplicity structure. - Jonathan D. Hauenstein; Bernard Mourrain; Ágnes Szántó (J. Symb. Comput., 2017)

A hybrid symbolic-numerical approach to the center-focus problem. - Adam Mahdi; Claudio Gomes Pessoa; Jonathan D. Hauenstein (J. Symb. Comput., 2017)

Algorithm 976: Bertini_real: Numerical Decomposition of Real Algebraic Curves and Surfaces. - Daniel A. Brake; Daniel J. Bates; Wenrui Hao; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (ACM Trans. Math. Softw., 2017)

polyTop: Software for Computing Topology of Smooth Real Surfaces. - Danielle A. Brake; Jonathan D. Hauenstein; Margaret H. Regan (ICMS, 2018)

Certifying Reality of Projections. - Jonathan D. Hauenstein; Avinash Kulkarni; Emre Can Sertöz; Samantha N. Sherman (ICMS, 2018)

Adaptive strategies for solving parameterized systems using homotopy continuation. - Jonathan D. Hauenstein; Margaret H. Regan (Appl. Math. Comput., 2018)

Optimal Configurations in Coverage Control with Polynomial Costs. - Shaunak D. Bopardikar; Dhagash Mehta; Jonathan D. Hauenstein (CoRR, 2018)

Numerical Computation of Galois Groups. - Jonathan D. Hauenstein; Jose Israel Rodriguez; Frank Sottile (Found. Comput. Math., 2018)

Certifying solutions to overdetermined and singular polynomial systems over ℚ. - Tulay Ayyildiz Akoglu; Jonathan D. Hauenstein; Ágnes Szántó (J. Symb. Comput., 2018)

Locating and Counting Equilibria of the Kuramoto Model with Rank-One Coupling. - Owen Coss; Jonathan D. Hauenstein; Hoon Hong; Daniel K. Molzahn (SIAM J. Appl. Algebra Geom., 2018)

Exceptional Stewart-Gough Platforms, Segre Embeddings, and the Special Euclidean Group. - Jonathan D. Hauenstein; Samantha N. Sherman; Charles W. Wampler (SIAM J. Appl. Algebra Geom., 2018)

Sampling Real Algebraic Varieties for Topological Data Analysis. - Emilie Dufresne; Parker B. Edwards; Heather A. Harrington; Jonathan D. Hauenstein (ICMLA, 2019)

Decomposing the Parameter Space of Biological Networks via a Numerical Discriminant Approach. - Heather A. Harrington; Dhagash Mehta; Helen M. Byrne; Jonathan D. Hauenstein (MC, 2019)

Solving Critical Point Conditions for the Hamming and Taxicab Distances to Solution Sets of Polynomial Equations. - Danielle A. Brake; Noah S. Daleo; Jonathan D. Hauenstein; Samantha N. Sherman (SYNASC, 2019)

Using Numerical Insights to Improve Symbolic Computations. - Jonathan D. Hauenstein (SYNASC, 2019)

Trifocal Relative Pose from Lines at Points and its Efficient Solution. - Ricardo Fabbri; Timothy Duff; Hongyi Fan; Margaret H. Regan; David da Costa de Pinho; Elias P. Tsigaridas; Charles Wrampler; Jonathan D. Hauenstein; Benjamin B. Kimia; Anton Leykin; Tomás Pajdla (CoRR, 2019)

Singular Value Decomposition of Complexes. - Danielle A. Brake; Jonathan D. Hauenstein; Frank-Olaf Schreyer; Andrew J. Sommese; Michael Eugene Stillman (SIAM J. Appl. Algebra Geom., 2019)

TRPLP - Trifocal Relative Pose From Lines at Points. - Ricardo Fabbri; Timothy Duff; Hongyi Fan; Margaret H. Regan; David da Costa de Pinho; Elias P. Tsigaridas; Charles W. Wampler; Jonathan D. Hauenstein; Peter J. Giblin; Benjamin B. Kimia; Anton Leykin; Tomás Pajdla (CVPR, 2020)

Evaluating and Differentiating a Polynomial Using a Pseudo-witness Set. - Jonathan D. Hauenstein; Margaret H. Regan (ICMS, 2020)

Using Monodromy to Statistically Estimate the Number of Solutions. - Jonathan D. Hauenstein; Samantha N. Sherman (IMAMR, 2020)

Certified Evaluations of Hölder Continuous Functions at Roots of Polynomials. - Parker B. Edwards; Jonathan D. Hauenstein; Clifford D. Smyth (MC, 2020)

Real monodromy action. - Jonathan D. Hauenstein; Margaret H. Regan (Appl. Math. Comput., 2020)

Smooth points on semi-algebraic sets. - Katherine Harris; Jonathan D. Hauenstein; Ágnes Szántó (ACM Commun. Comput. Algebra, 2020)

Designing Rotary Linkages for Polar Motions. - Aravind Baskar; Chang Liu 121; Mark M. Plecnik; Jonathan D. Hauenstein (IROS, 2021)

Excess intersections and numerical irreducible decompositions. - Daniel J. Bates; David Eklund; Jonathan D. Hauenstein; Chris Peterson 001 (SYNASC, 2021)

On some configurations of oppositely charged trapped vortices in the plane. - Emilie Dufresne; Heather A. Harrington; Jonathan D. Hauenstein; Panayotis G. Kevrekidis; Paolo Tripoli (Adv. Appl. Math., 2021)

Solving determinantal systems using homotopy techniques. - Jonathan D. Hauenstein; Mohab Safey El Din; Éric Schost; Thi Xuan Vu (J. Symb. Comput., 2021)

A numerical toolkit for multiprojective varieties. - Jonathan D. Hauenstein; Anton Leykin; Jose Israel Rodriguez; Frank Sottile (Math. Comput., 2021)

Finding Straight Line Generators Through the Approximate Synthesis of Symmetric Four-Bar Coupler Curves. - Aravind Baskar; Mark M. Plecnik; Jonathan D. Hauenstein (ARK, 2022)

AdaAnn: Adaptive Annealing Scheduler for Probability Density Approximation. - Emma R. Cobian; Jonathan D. Hauenstein; Fang Liu 006; Daniele E. Schiavazzi (CoRR, 2022)

Some interesting birational morphisms of smooth affine quadric 3-folds. - Cinzia Bisi; Jonathan D. Hauenstein; Tuyen Trung Truong (CoRR, 2022)

Probabilistic Saturations and Alt's Problem. - Jonathan D. Hauenstein; Martin Helmer (Exp. Math., 2022)

The Loss Surface of Deep Linear Networks Viewed Through the Algebraic Geometry Lens. - Dhagash Mehta; Tianran Chen; Tingting Tang; Jonathan D. Hauenstein (IEEE Trans. Pattern Anal. Mach. Intell., 2022)

On Computing the Nonlinearity Interval in Parametric Semidefinite Optimization. - Jonathan D. Hauenstein; Ali Mohammad Nezhad; Tingting Tang; Tamás Terlaky (Math. Oper. Res., 2022)

NCQS: Nonlinear Convex Quadrature Surrogate Hyperparameter Optimization. - Sophia J. Abraham; Kehelwala Dewage Gayan Maduranga; Jeffery Kinnison; Jonathan D. Hauenstein; Walter J. Scheirer (ICCV (Workshops), 2023)

Output Mode Switching for Parallel Five-bar Manipulators Using a Graph-based Path Planner. - Parker B. Edwards; Aravind Baskar; Caroline Hills; Mark M. Plecnik; Jonathan D. Hauenstein (ICRA, 2023)

Numerical Nonlinear Algebra. - Daniel J. Bates; Paul Breiding; Tianran Chen; Jonathan D. Hauenstein; Anton Leykin; Frank Sottile (CoRR, 2023)

HomOpt: A Homotopy-Based Hyperparameter Optimization Method. - Sophia J. Abraham; Kehelwala D. G. Maduranga; Jeffery Kinnison; Zachariah Carmichael; Jonathan D. Hauenstein; Walter J. Scheirer (CoRR, 2023)

Machine learning the real discriminant locus. - Edgar A. Bernal; Jonathan D. Hauenstein; Dhagash Mehta; Margaret H. Regan; Tingting Tang (J. Symb. Comput., 2023)

Trifocal Relative Pose From Lines at Points. - Ricardo Fabbri; Timothy Duff; Hongyi Fan; Margaret H. Regan; David da Costa de Pinho; Elias P. Tsigaridas; Charles W. Wampler; Jonathan D. Hauenstein; Peter J. Giblin; Benjamin B. Kimia; Anton Leykin; Tomás Pajdla (IEEE Trans. Pattern Anal. Mach. Intell., 2023)

Special issue on Algebraic Geometry and Machine Learning. - Jonathan D. Hauenstein; Yang-Hui He; Ilias S. Kotsireas; Dhagash Mehta; Tingting Tang (J. Symb. Comput., 2023)

Computing Geometric Feature Sizes for Algebraic Manifolds. - Sandra Di Rocco; Parker B. Edwards; David Eklund; Oliver Gäfvert; Jonathan D. Hauenstein (SIAM J. Appl. Algebra Geom., 2023)

Robust Numerical Algebraic Geometry. - Emma R. Cobian; Jonathan D. Hauenstein; Charles W. Wampler (CoRR, 2024)

Enhancing Ecological Monitoring with Multi-Objective Optimization: A Novel Dataset and Methodology for Segmentation Algorithms. - Sophia J. Abraham; Jin Huang; Brandon RichardWebster; Michael Milford; Jonathan D. Hauenstein; Walter J. Scheirer (CoRR, 2024)

On computing local monodromy and the numerical local irreducible decomposition. - Parker B. Edwards; Jonathan D. Hauenstein (CoRR, 2024)

On parametric semidefinite programming with unknown boundaries. - Jonathan D. Hauenstein; Tingting Tang (J. Symb. Comput., 2024)

LINFA: a Python library for variational inference with normalizing flow and annealing. - Yu Wang; Emma R. Cobian; Jubilee Lee; Fang Liu 006; Jonathan D. Hauenstein; Daniele E. Schiavazzi (J. Open Source Softw., 2024)

A Numerical Method for Solving Elliptic Equations on Real Closed Algebraic Curves and Surfaces. - Wenrui Hao; Jonathan D. Hauenstein; Margaret H. Regan; Tingting Tang (J. Sci. Comput., 2024)

Max-convolution through numerics and tropical geometry. - Taylor Brysiewicz; Jonathan D. Hauenstein; Caroline Hills (Numer. Algorithms, 2024)

Wavelet-Based Mechanistic Interpretability of Vision Transformers via Frequency-Aware Ablations. - Sophia J. Abraham; Jonathan D. Hauenstein; Walter J. Scheirer (CVPR Workshops, 2025)

Branch points of homotopies: Distribution and probability of failure. - Jonathan D. Hauenstein; Caroline Hills; Andrew J. Sommese; Charles W. Wampler (Appl. Math. Comput., 2025)

Geometry of Continuous Adjoint Newton's Method for Bivariate Quadratics. - Jonathan D. Hauenstein; Caroline Hills; Hoon Hong; Francisco Ponce Carrión (Maple Trans., 2025)

Towards Fair and Robust Face Parsing for Generative AI: A Multi-Objective Approach. - Sophia J. Abraham; Jonathan D. Hauenstein; Walter J. Scheirer (CoRR, 2025)