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· 제목 : Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Paperback) 
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 선형/비선형 프로그래밍
· ISBN : 9780898713640
· 쪽수 : 394쪽
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 선형/비선형 프로그래밍
· ISBN : 9780898713640
· 쪽수 : 394쪽
목차
- Preface to the Classics edition
- Preface
- Chapter 1: Introduction. Problems to be considered
- Characteristics of “real-world” problems
- Finite-precision arithmetic and measurement of error
- Exercises
- Chapter 2: Nonlinear Problems in One Variable. What is not possible
- Newton’s method for solving one equation in one unknown
- Convergence of sequences of real numbers
- Convergence of Newton’s method
- Globally convergent methods for solving one equation in one unknown
- Methods when derivatives are unavailable
- Minimization of a function of one variable
- Exercises
- Chapter 3: Numerical Linear Algebra Background. Vector and matrix norms and orthogonality
- Solving systems of linear equations—matrix factorizations
- Errors in solving linear systems
- Updating matrix factorizations
- Eigenvalues and positive definiteness
- Linear least squares
- Exercises
- Chapter 4: Multivariable Calculus Background
- Derivatives and multivariable models
- Multivariable finite-difference derivatives
- Necessary and sufficient conditions for unconstrained minimization
- Exercises
- Chapter 5: Newton's Method for Nonlinear Equations and Unconstrained Minimization. Newton’s method for systems of nonlinear equations
- Local convergence of Newton’s method
- The Kantorovich and contractive mapping theorems
- Finite-difference derivative methods for systems of nonlinear equations
- Newton’s method for unconstrained minimization
- Finite-difference derivative methods for unconstrained minimization
- Exercises
- Chapter 6: Globally Convergent Modifications of Newton’s Method. The quasi-Newton framework
- Descent directions
- Line searches
- The model-trust region approach
- Global methods for systems of nonlinear equations
- Exercises
- Chapter 7: Stopping, Scaling, and Testing. Scaling
- Stopping criteria
- Testing
- Exercises
- Chapter 8: Secant Methods for Systems of Nonlinear Equations. Broyden’s method
- Local convergence analysis of Broyden’s method
- Implementation of quasi-Newton algorithms using Broyden’s update
- Other secant updates for nonlinear equations
- Exercises
- Chapter 9: Secant Methods for Unconstrained Minimization. The symmetric secant update of Powell
- Symmetric positive definite secant updates
- Local convergence of positive definite secant methods
- Implementation of quasi-Newton algorithms using the positive definite secant update
- Another convergence result for the positive definite secant method
- Other secant updates for unconstrained minimization
- Exercises
- Chapter 10: Nonlinear Least Squares. The nonlinear least-squares problem
- Gauss-Newton-type methods
- Full Newton-type methods
- Other considerations in solving nonlinear least-squares problems
- Exercises
- Chapter 11: Methods for Problems with Special Structure. The sparse finite-difference Newton method
- Sparse secant methods
- Deriving least-change secant updates
- Analyzing least-change secant methods
- Exercises
- Appendix A: A Modular System of Algorithms for Unconstrained Minimization and Nonlinear Equations (by Robert Schnabel)
- Appendix B: Test Problems (by Robert Schnabel)
- References
- Author Index
- Subject Index.
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