International Congress on Mathematical Software 2026

14. Symbolic-Numeric Computation

Session Organizers:

• Rob Corless (Western University)
• Jürgen Gerhard (Maplesoft)
• Erik Postma (OpenTeams)

Session Abstract:

This session is about any kind of computation on the boundary between symbolic and numerical algorithms. The definition of “symbolic-numeric” will be interpreted fairly broadly.

Topics (including, but not limited to):

• Overview of symbolic-numeric computation
• Certified arbitrary-precision
• Numeric computation with guaranteed error bounds
• Interval arithmetic and Taylor models
• Symbolic-numeric linear algebra
• Symbolic-numeric methods for polynomial systems
• Symbolic-numeric methods for differential equations
• Post-certification of purely numerical algorithms
• Employing numerical algorithms to speed up symbolic computation

Call for Abstracts

Session Talks:

• Introductory Presentation Hybrid Symbolic-Numeric Computing: A Personal View, Rob Corless (Western University)
• Computing Periodic Golay Pairs Using SAT Solvers, Bernhard Andraschko (Universität Passau), Ilias Kotsireas (Wilfrid Laurier University), Martin Kreuzer (Universität Passau)
• Mathematical Software for the Evaluation of Distribution Functions of Quadratic Forms of Gaussian Random Variables, Denis Arzelier (LAAS-CNRS), Florent Bréhard (Université de Lille), Mioara Joldes (LAAS-CNRS)
• Eigensolvers for polynomial roots and tensor decomposition, Enrica Barrilli (Centre Inria d'Université Côte d'Azur) and Bernard Mourrain (Centre Inria d'Université Côte d'Azur)
• Mixed volume and ramification points of polyhedral homotopies, Joseph Cummings (University of Edinburgh) and Jonathan D. Hauenstein (University of Notre Dame)
• Certified Symbolic-Numeric Algorithms for Critical Engineering Applications, Alexander Demin (HSE University), Christina Katsamaki (Centre Inria de Paris), Fabrice Rouillier (Centre Inria de Paris)
• Semi-Heuristic Acceleration of Near-Optimal Black Box Polynomial Root-Finders, Soo Go (The City University of New York) and Victor Y. Pan (The City University of New York)
• Computing the Eigenvalues of QM-Matrices and Q^1,2-Matrices, Laureano Gonzalez-Vega (CUNEF Universidad)
• Belyi map verification using certified path tracking, Alexandre Guillemot (INRIA Saclay) and John Voigt (Dartmouth College)
• Numerical Elimination and Parameter Space Exploration, Oskar Henriksson (Max Planck Institute of Molecular Cell Biology and Genetics)
• Approximating periodic orbits with algebraic curves and related minimal problems, Ruiqi Huang (Georgia Tech) and Anton Leykin (Georgia Tech)
• Newton's Method for Real Powered Series using PHCpack and phcpy, Katie Kruzan (University of Illinois at Chicago) and Jan Verschelde (University of Illinois at Chicago)
• Parallel Certification of Roots of Polynomial Systems, David Johnson (Western University) and Taylor Brysiewicz (Western University)
• Tensor Optimization Framework for Sums-of-Squares Certification, Tanmaya Karmarkar (The University of British Columbia), Yves Lucet (The University of British Columbia), Narendra Karmarkar
• Randomized Algorithms for Verifying Monodromy Groups, Juhee Kim (Western University) and Taylor Brysiewicz (Western University)
• Certifying algebraic structures via interval arithmetic, Kisun Lee (Clemson University)
• Computer-assisted discovery and proofs of compatibility conditions for three projective cameras, Anton Leykin (Georgia Tech)
• ADTAYL: Taylor Series, ODEs, and Lie Derivatives in MATLAB, Ned Nedialkov (McMaster University)
• Holonomic gradient method - a symbolic-numeric method to evaluate integral with parameters, N. Takayama, T. Yaguchi, Y. Zhang
• Taylor Tubes: A Technique to Improve the Speed and Accuracy of Validated IVP Algorithms, Bingwei Zhang (The Courant Institute of Mathematical Sciences) and Chee Yap (The Courant Institute of Mathematical Sciences)