无约束最优化与非线性方程的数值方法 = Numerical methods for unconstrained optimization and nonlinear equations 🔍
J.E.Dennis等编著
北京:科学出版社, Guo wai shu xue ming zhu xi lie ;v42, Ying yin ban, Beijing, 2009
中文 [zh] · PDF · 35.5MB · 2009 · 📗 未知类型的图书 · 🚀/duxiu/upload · Save
描述
目录 8
PREFACE TO THE CLASSICS EDITION 12
PREFACE 14
1 INTRODUCTION 18
1.1 Problems to be considered 18
1.2 Characteristics of "real-world" problems 21
1.3 Finite-precision arithmetic and measurement of error 26
1.4 Exercises 29
2 NONLINEAR PROBLEMS IN ONE VARIABLE 31
2.1 What is not possible 31
2.2 Newton's method for solving one equation in one unknown 32
2.3 Convergence of sequences of real numbers 35
2.4 Convergence of Newton's method 37
2.5 Globally convergent methods for solving one equation in one unknown 40
2.6 Methods when derivatives are unavailable 43
2.7 Minimization of a function of one variable 48
2.8 Exercises 52
3 NUMERICAL LINEAR ALGEBRA BACKGROUND 56
3.1 Vector and matrix norms and orthogonality 57
3.2 Solving systems of linear equations-matrix factorizations 63
3.3 Errors in solving linear systems 67
3.4 Updating matrix factorizations 71
3.5 Eigenvalues and positive definiteness 74
3.6 Linear least squares 76
3.7 Exercises 82
4 MULTIVARIABLE CALCULUS BACKGROUND 85
4.1 Derivatives and multivariable models 85
4.2 Multivariable finite-difference derivatives 93
4.3 Necessary and sufficient conditions for unconstrained minimization 96
4.4 Exercises 99
5 NEWTON'S METHOD FOR NONLINEAR EQUATIONS AND UNCONSTRAINED MINIMIZATION 102
5.1 Newton's method for systems of nonlinear equations 102
5.2 Local convergence of Newton's method 105
5.3 The Kantorovich and contractive mapping theorems 108
5.4 Finite-difference derivative methods for systems of nonlinear equations 110
5.5 Newton's method for unconstrained minimization 115
5.6 Finite-difference derivative methods for unconstrained minimization 119
5.7 Exercises 123
6 GLOBALLY CONVERGENT MODIFICATIONS OF NEWTON'S METHOD 127
6.1 The quasi-Newton framework 128
6.2 Descent directions 129
6.3 Line searches 132
6.3.1 Convergence results for properly chosen steps 136
6.3.2 Step selection by backtracking 142
6.4 The model-trust region approach 145
6.4.1 The locally constrained optimal ("hook") step 150
6.4.2 The double dogleg step 155
6.4.3 Updating the trust region 159
6.5 Global methods for systems of nonlinear equations 163
6.6 Exercises 168
7 STOPPING, SCALING, AND TESTING 171
7.1 Scaling 171
7.1 Scaling 175
7.3 Testing 177
7.4 Exercises 180
8 SECANT METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS 184
8.1 Broyden's method 185
8.2 Local convergence analysis of Broyden's method 190
8.3 Implementation of quasi-Newton algorithms using Broyden's update 202
8.4 Other secant updates for nonlinear equations 205
8.5 Exercises 206
9 SECANT METHODS FOR UNCONSTRAINED MINIMIZATION 210
9.1 The symmetric secant update of Powell 211
9.2 Symmetric positive definite secant updates 214
9.3 Local convergence of positive definite secant methods 219
9.4 Implementation of quasi-Newton algorithms using the positive definite secant update 224
9.5 Another convergence result for the positive definite secant method 226
9.6 Other secant updates for unconstrained minimization 227
9.7 Exercises 228
10 NONLINEAR LEAST SQUARES 234
10.1 The nonlinear least-squares problem 234
10.2 Gauss-Newton-type methods 237
10.3 Full Newton-type methods 244
10.4 Other considerations in solving nonlinear least-squares problems 249
10.5 Exercise 252
11 METHODS FOR PROBLEMS WITH SPECIAL STRUCTURE 255
11.1 The sparse finite-difference Newton method 256
11.2 Sparse secant methods 258
11.3 Deriving least-change secant updates 262
11.4 Analyzing least-change secant methods 267
11.5 Exercises 272
A APPENDIX: A MODULAR SYSTEM OF ALGORITHMS FOR UNCONSTRAINED MINIMIZATION AND NONLINEAR EQUATIONS(by Robert Schnabel) 275
B APPENDIX: TEST PROBLEMS (by Robert Schnabel) 377
REFERENCES 380
AUTHOR INDEX 387
SUBJECT INDEX 389
参考文献 396
PREFACE TO THE CLASSICS EDITION 12
PREFACE 14
1 INTRODUCTION 18
1.1 Problems to be considered 18
1.2 Characteristics of "real-world" problems 21
1.3 Finite-precision arithmetic and measurement of error 26
1.4 Exercises 29
2 NONLINEAR PROBLEMS IN ONE VARIABLE 31
2.1 What is not possible 31
2.2 Newton's method for solving one equation in one unknown 32
2.3 Convergence of sequences of real numbers 35
2.4 Convergence of Newton's method 37
2.5 Globally convergent methods for solving one equation in one unknown 40
2.6 Methods when derivatives are unavailable 43
2.7 Minimization of a function of one variable 48
2.8 Exercises 52
3 NUMERICAL LINEAR ALGEBRA BACKGROUND 56
3.1 Vector and matrix norms and orthogonality 57
3.2 Solving systems of linear equations-matrix factorizations 63
3.3 Errors in solving linear systems 67
3.4 Updating matrix factorizations 71
3.5 Eigenvalues and positive definiteness 74
3.6 Linear least squares 76
3.7 Exercises 82
4 MULTIVARIABLE CALCULUS BACKGROUND 85
4.1 Derivatives and multivariable models 85
4.2 Multivariable finite-difference derivatives 93
4.3 Necessary and sufficient conditions for unconstrained minimization 96
4.4 Exercises 99
5 NEWTON'S METHOD FOR NONLINEAR EQUATIONS AND UNCONSTRAINED MINIMIZATION 102
5.1 Newton's method for systems of nonlinear equations 102
5.2 Local convergence of Newton's method 105
5.3 The Kantorovich and contractive mapping theorems 108
5.4 Finite-difference derivative methods for systems of nonlinear equations 110
5.5 Newton's method for unconstrained minimization 115
5.6 Finite-difference derivative methods for unconstrained minimization 119
5.7 Exercises 123
6 GLOBALLY CONVERGENT MODIFICATIONS OF NEWTON'S METHOD 127
6.1 The quasi-Newton framework 128
6.2 Descent directions 129
6.3 Line searches 132
6.3.1 Convergence results for properly chosen steps 136
6.3.2 Step selection by backtracking 142
6.4 The model-trust region approach 145
6.4.1 The locally constrained optimal ("hook") step 150
6.4.2 The double dogleg step 155
6.4.3 Updating the trust region 159
6.5 Global methods for systems of nonlinear equations 163
6.6 Exercises 168
7 STOPPING, SCALING, AND TESTING 171
7.1 Scaling 171
7.1 Scaling 175
7.3 Testing 177
7.4 Exercises 180
8 SECANT METHODS FOR SYSTEMS OF NONLINEAR EQUATIONS 184
8.1 Broyden's method 185
8.2 Local convergence analysis of Broyden's method 190
8.3 Implementation of quasi-Newton algorithms using Broyden's update 202
8.4 Other secant updates for nonlinear equations 205
8.5 Exercises 206
9 SECANT METHODS FOR UNCONSTRAINED MINIMIZATION 210
9.1 The symmetric secant update of Powell 211
9.2 Symmetric positive definite secant updates 214
9.3 Local convergence of positive definite secant methods 219
9.4 Implementation of quasi-Newton algorithms using the positive definite secant update 224
9.5 Another convergence result for the positive definite secant method 226
9.6 Other secant updates for unconstrained minimization 227
9.7 Exercises 228
10 NONLINEAR LEAST SQUARES 234
10.1 The nonlinear least-squares problem 234
10.2 Gauss-Newton-type methods 237
10.3 Full Newton-type methods 244
10.4 Other considerations in solving nonlinear least-squares problems 249
10.5 Exercise 252
11 METHODS FOR PROBLEMS WITH SPECIAL STRUCTURE 255
11.1 The sparse finite-difference Newton method 256
11.2 Sparse secant methods 258
11.3 Deriving least-change secant updates 262
11.4 Analyzing least-change secant methods 267
11.5 Exercises 272
A APPENDIX: A MODULAR SYSTEM OF ALGORITHMS FOR UNCONSTRAINED MINIMIZATION AND NONLINEAR EQUATIONS(by Robert Schnabel) 275
B APPENDIX: TEST PROBLEMS (by Robert Schnabel) 377
REFERENCES 380
AUTHOR INDEX 387
SUBJECT INDEX 389
参考文献 396
备选标题
Foreign mathematical classics series (continued) (photocopy) 42: unconstrained optimization and nonlinear equations. numerical methods(Chinese Edition)
备选标题
Numerical methods for unconstrained optimization and nonlinear equations : Optimization and Nonlinear Equations
备选标题
无约束最优化与非线性方程的数值方法 : [英文本
备选作者
J. E. Dennis Jr, Robert B. Schnabel[编著; Nnis De; Hnabel Sc
备选作者
John E. Dennis; Robert B. Schnabel
备选作者
MEI DAN NI SI Dennis J.E. DENG
备选作者
(美) Dennis, J. E. Jr
备选作者
Adobe Acrobat 7.0
备用出版商
Sciencep ; Society for Industrial and Applied Mathematics
备用出版商
Science Press
备用版本
Guo wai shu xue ming zhu xi lie, 42, Ying yin ban, Bei jing, 2009
备用版本
China, People's Republic, China
备用版本
Beijing, Philadelphia, ©2009
备用版本
1, 国外数学名著系列, 2009-01
元数据中的注释
producers:
Adobe Acrobat 7.0 Paper Capture Plug-in
Adobe Acrobat 7.0 Paper Capture Plug-in
开源日期
2025-10-27
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