[BOOK][B] The Numerical solution of systems of polynomials arising in engineering and science

AJ Sommese, CW Wampler - 2005 - books.google.com
Written by the founders of the new and expanding field of numerical algebraic geometry, this
is the first book that uses an algebraic-geometric approach to the numerical solution of …

[BOOK][B] Numerically solving polynomial systems with Bertini

Systems of polynomial equations are a common occurrence in problem formulations in
engineering, science, and mathematics. Solution sets of such systems, ie, algebraic sets, are …

[BOOK][B] Solving polynomial systems using continuation for engineering and scientific problems

A Morgan - 2009 - SIAM
This is an introduction to “polynomial continuation,” which is used to compute the solutions
to systems of polynomial equations. The book shows how to solve practical problems but …

Numerical algebraic geometry and algebraic kinematics

CW Wampler, AJ Sommese - Acta Numerica, 2011 - cambridge.org
In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism
spaces) are introduced. This provides a common schema for many kinds of problems that …

Recent advances in computational methods for the power flow equations

D Mehta, DK Molzahn, K Turitsyn - 2016 American Control …, 2016 - ieeexplore.ieee.org
The power flow equations are at the core of most of the computations for designing and
operating electric grids. This system of multivariate nonlinear equations relate the power …

Minimizing polynomial functions

PA Parrilo, B Sturmfels - arxiv preprint math/0103170, 2001 - arxiv.org
We compare algorithms for global optimization of polynomial functions in many variables. It
is demonstrated that existing algebraic methods (Gr\" obner bases, resultants, homotopy …

Solving polynomial systems via homotopy continuation and monodromy

T Duff, C Hill, A Jensen, K Lee, A Leykin… - IMA Journal of …, 2019 - academic.oup.com
We study methods for finding the solution set of a generic system in a family of polynomial
systems with parametric coefficients. We present a framework for describing monodromy …

Solving polynomial systems by homotopy continuation methods

TY Li - Computer mathematics (Tian**, 1991), 1993 - World Scientific
Solving polynomial systems by homotopy continuation methods Page 29 18 Computer
Mathematics Proc. of the Special Program at Nankai Institute of Mathematics January 1991-June …

Newton's method with deflation for isolated singularities of polynomial systems

A Leykin, J Verschelde, A Zhao - Theoretical Computer Science, 2006 - Elsevier
We present a modification of Newton's method to restore quadratic convergence for isolated
singular solutions of polynomial systems. Our method is symbolic–numeric: we produce a …

[BOOK][B] Solving polynomial equations

A Dickenstein - 2005 - Springer
The subject of this book is the solution of polynomial equations, that is, systems of
(generally) non-linear algebraic equations. This study is at the heart of several areas of …