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Numerical Solution of Systems of Nonlinear Algebraic Equations.

By: Byrne, George D.
Contributor(s): Hall, Charles A.
Material type: TextTextSeries: eBooks on Demand.Publisher: Burlington : Elsevier Science, 2014Description: 1 online resource (430 p.).ISBN: 9781483269306.Subject(s): Equations -- Numerical solutions -- CongressesGenre/Form: Electronic books.Additional physical formats: Print version:: Numerical Solution of Systems of Nonlinear Algebraic EquationsDDC classification: 512.9/42 | 512.942 Online resources: Click here to view this ebook.
Contents:
Front Cover; Numerical Solution of Systems of Nonlinear Algebraic Equations; Copyright Page; Table of Contents; CONTRIBUTORS; PREFACE; CHAPTER 1. NONLINEAR ALGEBRAIC EQUATIONS IN CONTINUUM MECHANICS; 1. Introduction; 2. Polynomials with Complex Coefficients; 3. Simultaneous Polynomials with Real Coefficients; 4. Transcendental Equations; 5. Polynomial Equations; 7. Algebraic Equations in Numerical Analysis; References; CHAPTER 2. THE NUMERICAL SOLUTION OF QUASILINEAR ELLIPTIC EQUATIONS; 1. Introduction; 2. The Numerical Solution of Some Quasilinear Elliptic Differential Equations
3. Two Nonlinear Diffusion ProblemsReferences; CHAPTER 3. NONLINEAR SYSTEMS IN SEMI-INFINITE PROGRAMMING; 1. Introduction; 2. An illustrative example; 3. General results on semi-infinite programs; 4. Numerical solution; References; CHAPTER 4. ON THE SOLUTION OF LARGE SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS WITH SPARSE, POSITIVE DEFINITE MATRICES; 1. Introduction; 2. The Basic Iterative Methods; 3. Convergence Results for the Basic Methods; 4. Semi-iterative Methods and Second-degree Methods; 5. Application to the Solution of Elliptic Boundary Value Problems; 6. Other Methods; References
CHAPTER 5. SOME COMPUTATIONAL TECHNIQUES FOR THE NONLINEAR LEAST SQUARES PROBLEM1. Introduction; 2. The Methods in General; 3. The Particular Methods; 4. Conclusions; References; CHAPTER 6. THE PROBLEM OF MINIMIZING NONLINEAR FUNCTIONALS; 1. Introduction; 2. Sufficient Conditions for Convergence; 3. The Quadratic Functional; 4. The Algorithm; 5. Numerical Examples; References; CHAPTER 7. QUASI-NEWTON, OR MODIFICATION METHODS; 1. Introduction; 2. Motivation and Implementation; 3. General Nonlinear Systems; 4. Least Squares Problems; 5. The Unconstrained Optimization Problem; 6. Symmetrization
7. Other ApplicationsReferences; CHAPTER 8. COMPUTER ORIENTED ALGORITHMS FOR SOLVING SYSTEMS OF SIMULTANEOUS NONLINEAR ALGEBRAIC EQUATIONS; 1. Introduction; 2. Methods for Use with Arbitrary or Poor Initial Guesses; 3. Some Methods Which Are Guaranteed To Converge; 4. A Rapidly Convergent Local Technique - Brown's Method; 5. A Local, Second Order Convergence Theorem for Brown's Method; 6. The Choice of hn in the Computer Implementation of Brown's Method; 7. Computational Efficiency and Numerical Results for Brown's Method; 8. On Minimizing Computational Effort: The Samanskii Idea
9. Deflation Techniques for the Calculation of Further Solutions of a Nonlinear SystemReferences; CHAPTER 9. ON THE CHOICE OF RELAXATION PARAMETERS FOR NONLINEAR PROBLEMS; 1. Introduction; 2. The Problem; 3. The Parameter δo; 4. A Convergence Result; 5. Group Relaxation; 6. Applications; 7. Criterion for Bounded Level Sets; 8. Examples; References; CHAPTER 10. THE CONTRACTOR THEORY OF SOLVING EQUATIONS; 0. Introduction; 1. Inverse Derivatives and Contractors; 2. Directional Contractors; 3. Contractors with Nonlinear Majorant Functions; References; SUBJECT INDEX
Summary: Numerical Solution of Systems of Nonlinear Algebraic Equations
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Front Cover; Numerical Solution of Systems of Nonlinear Algebraic Equations; Copyright Page; Table of Contents; CONTRIBUTORS; PREFACE; CHAPTER 1. NONLINEAR ALGEBRAIC EQUATIONS IN CONTINUUM MECHANICS; 1. Introduction; 2. Polynomials with Complex Coefficients; 3. Simultaneous Polynomials with Real Coefficients; 4. Transcendental Equations; 5. Polynomial Equations; 7. Algebraic Equations in Numerical Analysis; References; CHAPTER 2. THE NUMERICAL SOLUTION OF QUASILINEAR ELLIPTIC EQUATIONS; 1. Introduction; 2. The Numerical Solution of Some Quasilinear Elliptic Differential Equations

3. Two Nonlinear Diffusion ProblemsReferences; CHAPTER 3. NONLINEAR SYSTEMS IN SEMI-INFINITE PROGRAMMING; 1. Introduction; 2. An illustrative example; 3. General results on semi-infinite programs; 4. Numerical solution; References; CHAPTER 4. ON THE SOLUTION OF LARGE SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS WITH SPARSE, POSITIVE DEFINITE MATRICES; 1. Introduction; 2. The Basic Iterative Methods; 3. Convergence Results for the Basic Methods; 4. Semi-iterative Methods and Second-degree Methods; 5. Application to the Solution of Elliptic Boundary Value Problems; 6. Other Methods; References

CHAPTER 5. SOME COMPUTATIONAL TECHNIQUES FOR THE NONLINEAR LEAST SQUARES PROBLEM1. Introduction; 2. The Methods in General; 3. The Particular Methods; 4. Conclusions; References; CHAPTER 6. THE PROBLEM OF MINIMIZING NONLINEAR FUNCTIONALS; 1. Introduction; 2. Sufficient Conditions for Convergence; 3. The Quadratic Functional; 4. The Algorithm; 5. Numerical Examples; References; CHAPTER 7. QUASI-NEWTON, OR MODIFICATION METHODS; 1. Introduction; 2. Motivation and Implementation; 3. General Nonlinear Systems; 4. Least Squares Problems; 5. The Unconstrained Optimization Problem; 6. Symmetrization

7. Other ApplicationsReferences; CHAPTER 8. COMPUTER ORIENTED ALGORITHMS FOR SOLVING SYSTEMS OF SIMULTANEOUS NONLINEAR ALGEBRAIC EQUATIONS; 1. Introduction; 2. Methods for Use with Arbitrary or Poor Initial Guesses; 3. Some Methods Which Are Guaranteed To Converge; 4. A Rapidly Convergent Local Technique - Brown's Method; 5. A Local, Second Order Convergence Theorem for Brown's Method; 6. The Choice of hn in the Computer Implementation of Brown's Method; 7. Computational Efficiency and Numerical Results for Brown's Method; 8. On Minimizing Computational Effort: The Samanskii Idea

9. Deflation Techniques for the Calculation of Further Solutions of a Nonlinear SystemReferences; CHAPTER 9. ON THE CHOICE OF RELAXATION PARAMETERS FOR NONLINEAR PROBLEMS; 1. Introduction; 2. The Problem; 3. The Parameter δo; 4. A Convergence Result; 5. Group Relaxation; 6. Applications; 7. Criterion for Bounded Level Sets; 8. Examples; References; CHAPTER 10. THE CONTRACTOR THEORY OF SOLVING EQUATIONS; 0. Introduction; 1. Inverse Derivatives and Contractors; 2. Directional Contractors; 3. Contractors with Nonlinear Majorant Functions; References; SUBJECT INDEX

Numerical Solution of Systems of Nonlinear Algebraic Equations

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