Iterative solution of nonlinear equations in several variables / J. M. Ortega and W. C. Rheinboldt.

Format:

Book

Author/Creator:

Ortega, James M., 1932- author.

Rheinboldt, Werner C., author.

Series:

Computer science and applied mathematics.

Computer Science and Applied Mathematics

Language:

English

Subjects (All):

Iterative methods (Mathematics).

Equations--Numerical solutions.

Equations.

Physical Description:

1 online resource (593 p.)

Place of Publication:

San Diego, California ; London : Academic Press, Inc., 1970.

Language Note:

English

Summary:

Iterative Solution of Nonlinear Equations in Several Variables

Contents:

Front Cover; Iterative Solution of Nonlinear Equations in Several Variables; Copyright Page; Table of Contents; PREFACE; ACKNOWLEDGMENTS; GLOSSARY OF SYMBOLS; INTRODUCTION; PART I: BACKGROUND MATERIAL; CHAPTER 1. SAMPLE PROBLEMS; 1.1. TWO-POINT BOUNDARY VALUE PROBLEMS; 1.2. ELLIPTIC BOUNDARY VALUE PROBLEMS; 1.3. INTEGRAL EQUATIONS; 1.4. MINIMIZATION PROBLEMS; 1.5. TWO-DIMENSIONAL VARIATIONAL PROBLEMS; CHAPTER 2. LINEAR ALGEBRA; 2.1. A REVIEW OF BASIC MATRIX THEORY; 2.2. NORMS; 2.3. INVERSES; 2.4. PARTIAL ORDERING AND NONNEGATIVE MATRICES; CHAPTER 3. ANALYSIS

3.1. DERIVATIVES AND OTHER BASIC CONCEPTS3.2. MEAN-VALUE THEOREMS; 3.3. SECOND DERIVATIVES; 3.4. CONVEX FUNCTIONALS; PART II: NONCONSTRUCTIVE EXISTENCE THEOREMS; CHAPTER 4. GRADIENT MAPPINGS AND MINIMIZATION; 4.1. MINIMIZERS, CRITICAL POINTS, AND GRADIENT MAPPINGS; 4.2. UNIQUENESS THEOREMS; 4.3. EXISTENCE THEOREMS; 4.4. APPLICATIONS; CHAPTER 5. CONTRACTIONS AND THE CONTINUATION PROPERTY; 5.1. CONTRACTIONS; 5.2. THE INVERSE AND IMPLICITFUNCTION THEOREMS; 5.3. THE CONTINUATION PROPERTY; 5.4. MONOTONE OPERATORS AND OTHER APPLICATIONS; CHAPTER 6. THE DEGREE OF A MAPPING

6.1. ANALYTIC DEFINITION OF THE DEGREE6.2. PROPERTIES OF THE DEGREE; 6.3. BASIC EXISTENCE THEOREMS; 6.4. MONOTONE AND COERCIVE MAPPINGS; 6.5. APPENDIX. ADDITIONAL ANALYTIC RESULTS; PART III: ITERATIVE METHODS; CHAPTER 7. GENERAL ITERATIVE METHODS; 7.1. NEWTON'S METHOD AND SOME OF ITS VARIATIONS; 7.2. SECANT METHODS; 7.3. MODIFICATION METHODS; 7.4. GENERALIZED LINEAR METHODS; 7.5. CONTINUATION METHODS; 7.6. GENERAL DISCUSSION OF ITERATIVE METHODS; CHAPTER 8. MINIMIZATION METHODS; 8.1. PARABOLOID METHODS; 8.2. DESCENT METHODS; 8 3. STEPLENGTH ALGORITHMS; 8.4. CONJUGATE-DIRECTION METHODS

8.5. THE GAUSS-NEWTON AND RELATED METHODS8.6. APPENDIX 1. CONVERGENCE OF THE CONJUGATE GRADIENT AND THE DAVIDON-FLETCHER-POWELL ALGORITHMS FOR QUADRATIC FUNCTIONALS; 8.7. APPENDIX 2. SEARCH METHODS FOR ONE-DIMENSIONAL MINIMIZATION; PART IV: LOCAL CONVERGENCE; CHAPTER 9. RATES OF CONVERGENCE-GENERAL; 9.1. THE QUOTIENT CONVERGENCE FACTORS; 9.2. THE ROOT-CONVERGENCE FACTORS; 9.3. RELATIONS BETWEEN THE R AND Q CONVERGENCE FACTORS; CHAPTER 10. ONE-STEP STATIONARY METHODS; 10.1. BASIC RESULTS; 10.2. NEWTON'S METHOD AND SOME OF ITS MODIFICATIONS; 10.3. GENERALIZED LINEAR ITERATIONS

10.4. CONTINUATION METHODS10.5. APPENDIX. COMPARISON THEOREMS AND OPTIMAL w FOR SOR METHODS; CHAPTER 11. MULTISTEP METHODS AND ADDITIONAL ONE-STEP METHODS; 11.1. INTRODUCTION AND FIRST RESULTS; 11.2. CONSISTENT APPROXIMATIONS; 11.3. THE GENERAL SECANT METHOD; PART V: SEMILOCAL AND GLOBAL CONVERGENCE; CHAPTER 12. CONTRACTIONS AND NONLINEAR MAJORANTS; 12.1. SOME GENERALIZATIONS OF THE CONTRACTION THEOREM; 12.2. APPROXIMATE CONTRACTIONS AND SEQUENCESOF CONTRACTIONS; 12.3. ITERATED CONTRACTIONS AND NONEXPANSIONS; 12.4. NONLINEAR MAJORANTS; 12.5. MORE GENERAL MAJORANTS

12.6. NEWTON'S METHOD AND RELATED ITERATIONS

Notes:

Description based upon print version of record.

Includes bibliographical references and indexes.

Description based on print version record.

ISBN:

1-4832-7672-4