Atjaunināt sīkdatņu piekrišanu

Solving Nonlinear Equations with Newton's Method illustrated edition [Paperback]

  • Formāts: Paperback, 117 pages, height x width x depth: 229x152x6 mm, weight: 232 g, Illustrations
  • Sērija : Fundamentals of Algorithms No. 1
  • Izdošanas datums: 01-Jan-1987
  • Izdevniecība: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898715466
  • ISBN-13: 9780898715460
Citas grāmatas par šo tēmu:
  • Paperback
  • Cena: 75,46 €
  • Grāmatu piegādes laiks ir 3-4 nedēļas, ja grāmata ir uz vietas izdevniecības noliktavā. Ja izdevējam nepieciešams publicēt jaunu tirāžu, grāmatas piegāde var aizkavēties.
  • Daudzums:
  • Ielikt grozā
  • Piegādes laiks - 4-6 nedēļas
  • Pievienot vēlmju sarakstam
Solving Nonlinear Equations with Newton's Method illustrated editionPalielināt
  • Formāts: Paperback, 117 pages, height x width x depth: 229x152x6 mm, weight: 232 g, Illustrations
  • Sērija : Fundamentals of Algorithms No. 1
  • Izdošanas datums: 01-Jan-1987
  • Izdevniecība: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898715466
  • ISBN-13: 9780898715460
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780898715460.html
Keywords:
This brief book on Newton's method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. It contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages. The author covers both simple techniques for scalar problems as well as contemporary techniques (e.g. inexact Newton methods and Newton-Krylov techniques) for larger scale problems. This book is intended to complement Kelley's larger book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), which focuses on in-depth treatment of convergence theory, but does not discuss the details of solving particular problems, implementation in any particular language, or evaluating a solver for a given problem.
Preface xi
How to Get the Software xiii
1 Introduction 1(26)
1.1 What Is the Problem?
1(1)
1.1.1 Notation
1(1)
1.2 Newton's Method
2(3)
1.2.1 Local Convergence Theory
3(2)
1.3 Approximating the Jacobian
5(2)
1.4 Inexact Newton Methods
7(2)
1.5 Termination of the Iteration
9(2)
1.6 Global Convergence and the Armijo Rule
11(1)
1.7 A Basic Algorithm
12(3)
1.7.1 Warning!
14(1)
1.8 Things to Consider
15(2)
1.8.1 Human Time and Public Domain Codes
15(1)
1.8.2 The Initial Iterate
15(1)
1.8.3 Computing the Newton Step
16(1)
1.8.4 Choosing a Solver
16(1)
1.9 What Can Go Wrong?
17(3)
1.9.1 Nonsmooth Functions
17(1)
1.9.2 Failure to Converge
18(1)
1.9.3 Failure of the Line Search
19(1)
1.9.4 Slow Convergence
19(1)
1.9.5 Multiple Solutions
20(1)
1.9.6 Storage Problems
20(1)
1.10 Three Codes for Scalar Equations
20(4)
1.10.1 Common Features
21(1)
1.10.2 newtsol.m
21(1)
1.10.3 chordsol.m
22(1)
1.10.4 secant.m
23(1)
1.11 Projects
24(3)
1.11.1 Estimating the q-order
24(1)
1.11.2 Singular Problems
25(2)
2 Finding the Newton Step with Gaussian Elimination 27(30)
2.1 Direct Methods for Solving Linear Equations
27(1)
2.2 The Newton-Armijo Iteration
28(1)
2.3 Computing a Finite Difference Jacobian
29(4)
2.4 The Chord and Shamanskii Methods
33(1)
2.5 What Can Go Wrong?
34(1)
2.5.1 Poor Jacobians
34(1)
2.5.2 Finite Difference Jacobian Error
35(1)
2.5.3 Pivoting
35(1)
2.6 Using nsold.m
35(2)
2.6.1 Input to nsold.m
36(1)
2.6.2 Output from nsold.m
37(1)
2.7 Examples
37(13)
2.7.1 Arctangent Function
38(1)
2.7.2 A Simple Two-Dimensional Example
39(2)
2.7.3 Chandrasekhar H-equation
41(2)
2.7.4 A Two-Point Boundary Value Problem
43(4)
2.7.5 Stiff Initial Value Problems
47(3)
2.8 Projects
50(1)
2.8.1 Chandrasekhar H-equation
58
2.8.2 Nested Iteration
50(1)
2.9 Source Code for nsold.m
51(6)
3 Methods 57(23)
3.1 Krylov Methods for Solving Linear Equations
57(4)
3.1.1 GMRES
58
3.1.2 Low-Storage Krylov Methods
50(10)
3.1.3 Preconditioning
60(1)
3.2 Computing an Approximate Newton Step
61(2)
3.2.1 Products
61(1)
3.2.2 Preconditioning Nonlinear Equations
61(1)
3.2.3 Choosing the Forcing Term
62(1)
3.3 Preconditioners
63(1)
3.4 What Can Go Wrong?
64(1)
3.4.1 Failure of the Inner Iteration
64(1)
3.4.2 Loss of Orthogonality
64(1)
3.5 Using nsoli.m
65(1)
3.5.1 Input to nsoli.m
65(1)
3.5.2 Output from nsoli.m
65(1)
3.6 Examples
66(8)
3.6.1 Chandrasekhar H-equation
66(1)
3.6.2 The Ornstein-Zernike Equations
67(4)
3.6.3 Equation
71(2)
3.6.4 Time-Dependent Convection-Diffusion Equation
73(1)
3.7 Projects
74(2)
3.7.1 Krylov Methods and the Forcing Term
74(1)
3.7.2 Left and Right Preconditioning
74(1)
3.7.3 Two-Point Boundary Value Problem
74(1)
3.7.4 Making e Movie
75(1)
3.8 Source Code for nsoli.m
76(4)
4 Broyden's Method 80(17)
4.1 Convergence Theory
86(1)
4.2 An Algorithmic Sketch
86(1)
4.3 Computing the Broyden Computing Step and Update
87(2)
4.4 What Can Go Wrong?
89(1)
4.4.1 Failure of the Line Search
89(1)
4.4.2 Failure to Converge
89(1)
4.5 Using brsola.m
89(1)
4.5.1 Input to brsola.m
90(1)
4.5.2 Output from brsola.m
90(1)
4.6 Examples
90(3)
4.6.1 Chandrasekhar H-equation
91(1)
4.6.2 Convection-Diffusion Equation
91(2)
4.7 Source Code for brsola.m
93(4)
Bibliography 97(6)
Index 103