[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 …
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 …
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 …
to systems of polynomial equations. The book shows how to solve practical problems but …
Numerical algebraic geometry and algebraic kinematics
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 …
spaces) are introduced. This provides a common schema for many kinds of problems that …
Recent advances in computational methods for the power flow equations
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 …
operating electric grids. This system of multivariate nonlinear equations relate the power …
Minimizing polynomial functions
We compare algorithms for global optimization of polynomial functions in many variables. It
is demonstrated that existing algebraic methods (Gr\" obner bases, resultants, homotopy …
is demonstrated that existing algebraic methods (Gr\" obner bases, resultants, homotopy …
Solving polynomial systems via homotopy continuation and monodromy
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 …
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 …
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
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 …
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 …
(generally) non-linear algebraic equations. This study is at the heart of several areas of …