2023 - T3 - WS2 - Geometry of polynomial system solving, optimization and topology

Collection 2023 - T3 - WS2 - Geometry of polynomial system solving, optimization and topology

Organizer(s) D’Andrea, Carlos ; Lairez, Pierre ; Safey El Din, Mohab ; Schost, Éric ; Zhi, Lihong

Date(s) 16/10/2023 - 20/10/2023

linked URL https://indico.math.cnrs.fr/event/8114/

8 13

u-generation: solving systems of polynomials equation-by-equation

By Anton Leykin

We develop a new method that improves the efficiency of equation-by-equation homotopy continuation methods for solving polynomial systems. Our method is based on a novel geometric construction and reduces the total number of homotopy paths that must be numerically continued. These improvements may be applied to the basic algorithms of numerical algebraic geometry in the settings of both projective and multiprojective varieties. (This is joint work with T. Duff and J. I. Rodriguez.)

Information about the video

Date of publication 18/10/2023
Institution IHP
Language English
Audience Researchers, Graduate Students
Director(s) Alexandre Duplessis
Format MP4

Domain(s)

Algebraic Geometry

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

All the collection videos

published on October 16, 2023

Modular algorithms for computing triangular decompositions of polynomial systems

By Marc Moreno Maza

published on October 16, 2023

Chordal Graphs in Triangular Decomposition in Top-Down Style

By Chenqi Mou

published on October 16, 2023

Dimension results for sparse systems homogenized via rational polytopes

By Pierre-Jean Spaenlehauer

published on October 20, 2023

Recent advances in Gröbner basis algorithms and geometric applications

By Christian Eder

published on October 17, 2023

Polynomial Systems Arising in Paradoxical $6R$ Linkages

By Zijia Li

published on October 17, 2023

Positive solutions of parametric polynomial systems and biochemical reaction networks

By Elisenda Feliu

published on October 18, 2023

Some advances in numerical algebraic geometry for computing real solutions

By Jon Hauenstein

published on October 18, 2023

u-generation: solving systems of polynomials equation-by-equation

By Anton Leykin

published on October 19, 2023

Conormal Spaces and Whitney Stratifications

By Martin Helmer

published on October 19, 2023

Non-negativity and rational sums of squares over zero-dimensional varieties

By Teresa Krick

published on October 19, 2023

Sums of squares approximations in polynomial optimization: performance analysis and degree bounds

By Monique Laurent

published on October 19, 2023

Solving by duality

By Bernard Mourrain

published on October 20, 2023

The Wonderful Geometry of the Vandermonde map

By Cordian Riener

Copyright Carmin.tv 2024

Give feedback