Some computational methods for systems of nonlinear equations and systems of polynomial equations
type: Item
instance of: scholarly article
title: Some computational methods for systems of nonlinear equations and systems of polynomial equations
zbMATH Open document ID: 0759.65020
DOI: 10.1007/BF00122427
author: S. Singh
published in: Journal of Global Optimization
publication date: 1993-01-17T00:00:00Z
review text: The paper presents a survey of computational methods for solving systems of nonlinear equations and, in particular, systems of polynomial equations. The emphasis is laid on simplicial algorithms and homotopy methods and, in fact, the material on other methods only consists of relatively general observations. After introductory comments, simplicial algorithms and their application are discussed and Kuhn's method for finding all zeros of a polynomial is presented and analyzed. Then homotopy methods are introduced for general systems and considered in more detail for systems of polynomial equations. Some enhancements of known methods are suggested in the paper but no numerical details are included.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65H20
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 12Y05
zbMATH DE Number: 98693
zbMATH Keywords: pivoting algorithms
zbMATH Keywords: Nielsen fixed point theory
zbMATH Keywords: systems of nonlinear equations
zbMATH Keywords: systems of polynomial equations
zbMATH Keywords: simplicial algorithms
zbMATH Keywords: homotopy methods
zbMATH Keywords: Kuhn's method
zbMATH Keywords: zeros of a polynomial
reviewed by: Werner C. Rheinboldt
describes a project that uses: PITCON
describes a project that uses: praxis
MaRDI profile type: Publication
cites work: The Homotopy Continuation Method: Numerically Implementable Topological Procedures
cites work: A search routine for a Sperner simplex
cites work: Q3859594
cites work: Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations
cites work: Q3998344
cites work: Nielsen Numbers of Maps of Tori
cites work: An intuitionist correction of the fixed-point theorem on the sphere
cites work: Q5619504
cites work: Constructive proofs of theorems relating to:F(x) = y, with applications
cites work: Finding Zeroes of Maps: Homotopy Methods That are Constructive With Probability One
cites work: Minimal triangulation of the 4-cube
cites work: Q5588318
cites work: Q3917180
cites work: Q3941926
cites work: A course in triangulations for solving equations with deformations
cites work: Q4744214
cites work: A generalization of Tucker's combinatorial lemma with topological applications
cites work: Q4101353
cites work: Q3205183
cites work: Combinatorial Theorems on the Simplotope that Generalize Results on the Simplex and Cube
cites work: Determining All Solutions to Certain Systems of Nonlinear Equations
cites work: Finding all solutions to polynomial systems and other systems of equations
cites work: Q3870700
cites work: Q3662991
cites work: Q4134602
cites work: Q3250864
cites work: On the Least Number of Fixed Points
cites work: A generalization of Brouwer's fixed point theorem
cites work: Q4196372
cites work: A modification of todd's triangulationJ 3
cites work: Variable dimension algorithms: Basic theory, interpretations and extensions of some existing methods
cites work: Computation of all solutions to a system of polynomial equations
cites work: Q4138976
cites work: Sandwich method for finding fixed points
cites work: On the cost of computing roots of polynomials
cites work: On the Computation of Fixed Points in the Product Space of Unit Simplices and an Application to Noncooperative N Person Games
cites work: Simplicial Variable Dimension Algorithms for Solving the Nonlinear Complementarity Problem on a Product of Unit Simplices Using a General Labelling
cites work: Homotopy algorithm for symmetric eigenvalue problems
cites work: Triangulations for the cube
cites work: Q5605151
cites work: Q5510566
cites work: Q4000024
cites work: Q5652137
cites work: Cayley's problem and Julia sets
cites work: Q4692890
cites work: On the complexity of a piecewise linear algorithm for approximating roots of complex polynomials
cites work: On the cost of approximating all roots of a complex polynomial
cites work: Q3704827
cites work: Q3912504
cites work: Q5667781
cites work: On Paths Generated by Fixed Point Algorithms
cites work: A note on minimal triangulations of an n-cube
cites work: The Approximation of Fixed Points of a Continuous Mapping
cites work: Q4070959

Some computational methods for systems of nonlinear equations and systems of polynomial equations (cites work)
cites work: Q3674371

Some computational methods for systems of nonlinear equations and systems of polynomial equations (cites work)
cites work: A convergent process of price adjustment and global Newton methods

Some computational methods for systems of nonlinear equations and systems of polynomial equations (cites work)
cites work: The fundamental theorem of algebra and complexity theory

Some computational methods for systems of nonlinear equations and systems of polynomial equations (cites work)
cites work: On the efficiency of algorithms of analysis

Some computational methods for systems of nonlinear equations and systems of polynomial equations (cites work)
cites work: Q5522742

Some computational methods for systems of nonlinear equations and systems of polynomial equations (cites work)
cites work: Q3891456

Some computational methods for systems of nonlinear equations and systems of polynomial equations (cites work)
cites work: The computation of fixed points and applications

Some computational methods for systems of nonlinear equations and systems of polynomial equations (cites work)
cites work: Pivotal methods for computing equilibrium points: Unified approach and new restart algorithm

Some computational methods for systems of nonlinear equations and systems of polynomial equations (cites work)
cites work: Numerical Linear Algebra Aspects of Globally Convergent Homotopy Methods

Some computational methods for systems of nonlinear equations and systems of polynomial equations (cites work)
cites work: The octahedral algorithm, a new simplicial fixed point algorithm

Some computational methods for systems of nonlinear equations and systems of polynomial equations (cites work)
cites work: Topologic proofs of some combinatorial theorems

Some computational methods for systems of nonlinear equations and systems of polynomial equations (cites work)
cites work: Unknotting combinatorial balls