Journal ArticleDOI
Eine Methode zur berechnung sämtlicher Lösungen von Polynomgleichungssystemen
TLDR
In this article, a numerical method is given to compute all solutions of systemsT ofn polynomial equations inn unknowns on the only premises that the sets of solutions of these systems are finite.Abstract:
In this paper a numerical method is given to compute all solutions of systemsT ofn polynomial equations inn unknowns on the only premises that the sets of solutions of these systems are finite. The method employed is that of "embedding", i.e. the systemT is embedded in a set of systems which are successively solved, starting with one having solutions easily to compute and proceding toT in a finite series of steps. An estimation of the number of steps necessary is given. The practicability of the method is proved for all systemsT. Numerical examples and results are contained.read more
Citations
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Introduction to Numerical Continuation Methods
Eugene L. Allgower,Kurt Georg +1 more
TL;DR: The Numerical Continuation Methods for Nonlinear Systems of Equations (NCME) as discussed by the authors is an excellent introduction to numerical continuuation methods for solving nonlinear systems of equations.
Journal ArticleDOI
Solving the Kinematics of the Most General Six- and Five-Degree-of-Freedom Manipulators by Continuation Methods
Lung-Wen Tsai,A. P. Morgan +1 more
TL;DR: It is shown that the problem can be reduced to that of solving a system of eight second-degree equations in eight unknowns, it-is-fttrther-demrmstrate^-thafmis second- Degree system can be routinely solved using a continuation algorithm.
Journal ArticleDOI
A homotopy for solving general polynomial systems that respects m-homogeneous structures
TL;DR: A new method for defining a homotophy to find all solutions to a polynomial system, F(z) = 0, of n equations in n unknowns using a generic homotopy, which represents a significant advance over previous homotopies.
Journal ArticleDOI
Numerical solution of multivariate polynomial systems by homotopy continuation methods
TL;DR: In this article, the problem of finding all isolated solutions to polynomial equations in n unknown unknowns is studied. But their reliance on symbolic manipulation makes those methods seem somewhat unsuitable for all but small problems.
Journal ArticleDOI
Computing with polynomials given byblack boxes for their evaluations: Greatest common divisors, factorization, separation of numerators and denominators
Erich Kaltofen,Barry M. Trager +1 more
TL;DR: It is shown that within this black box representation the polynomial greatest common divisor and factorization problems, as well as the problem of extracting the numerator and denominator of a rational function, can all be solved in randomPolynomial-time.
References
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Iterative Solution of Large Linear Systems
TL;DR: The ASM preconditioner B is characterized by three parameters: C0, ρ(E) , and ω , which enter via assumptions on the subspaces Vi and the bilinear forms ai(·, ·) (the approximate local problems).
Book
Approximate Solution of Operator Equations
TL;DR: The theory of approximate methods for solving mathematical problems has been studied extensively in the literature, see as discussed by the authors for a survey of some of the most important results in functional analysis. But the authors' aim has not been to give an exhaustive account, even of the principal known results.