Some computational methods for systems of nonlinear equations and systems of polynomial equations

DOI10.1007/BF00122427zbMath0759.65020MaRDI QIDQ1201902

S. Singh

Publication date: 17 January 1993

Published in: Journal of Global Optimization (Search for Journal in Brave)

zbMATH Keywords

systems of polynomial equationszeros of a polynomialsystems of nonlinear equationshomotopy methodsNielsen fixed point theorysimplicial algorithmsKuhn's methodpivoting algorithms

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Real polynomials: location of zeros (26C10)

Uses Software

• PITCON
• praxis

Cites Work

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• Cayley's problem and Julia sets
• Homotopy algorithm for symmetric eigenvalue problems
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• A search routine for a Sperner simplex
• Unknotting combinatorial balls
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• A generalization of Brouwer's fixed point theorem
• On the cost of computing roots of polynomials
• Computation of all solutions to a system of polynomial equations
• On the complexity of a piecewise linear algorithm for approximating roots of complex polynomials
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• On the efficiency of algorithms of analysis
• Combinatorial Theorems on the Simplotope that Generalize Results on the Simplex and Cube
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• Simplicial Variable Dimension Algorithms for Solving the Nonlinear Complementarity Problem on a Product of Unit Simplices Using a General Labelling
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• Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations
• On the Least Number of Fixed Points
• The fundamental theorem of algebra and complexity theory
• The octahedral algorithm, a new simplicial fixed point algorithm
• Pivotal methods for computing equilibrium points: Unified approach and new restart algorithm
• On the Computation of Fixed Points in the Product Space of Unit Simplices and an Application to Noncooperative N Person Games
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• Constructive proofs of theorems relating to:F(x) = y, with applications
• On Paths Generated by Fixed Point Algorithms
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• Determining All Solutions to Certain Systems of Nonlinear Equations
• Finding all solutions to polynomial systems and other systems of equations
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• The Approximation of Fixed Points of a Continuous Mapping
• An intuitionist correction of the fixed-point theorem on the sphere
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