عنوان

Solving nonlinear equations with Newton's method /

0898715466

9780898715460

b716891

Solving nonlinear equations with Newton's method /

[Book]

C.T. Kelley.

Philadelphia :

Society for Industrial and Applied Mathematics,

©2003.

xiii, 104 pages :

illustrations ;

26 cm.

Fundamentals of algorithms

Includes bibliographical references (pages 97-102) and index.

1. Introduction -- 1.1. What is the problem? -- 1.2. Newton's method -- 1.3. Approximating the Jacobian -- 1.4. Inexact Newton methods -- 1.5. Termination of the iteration -- 1.6. Global convergence and the Armijo rule -- 1.7. A basic algorithm -- 1.8. Things to consider -- 1.9. What can go wrong? -- 1.10. Three codes for scalar equations -- 1.11. Projects -- 2. Finding the Newton step with Gaussian elimination -- 2.1. Direct methods for solving linear equations -- 2.2. The Newton-Armijo iteration -- 2.3. Computing a finite difference Jacobian -- 2.4. The chord and shamanskii methods -- 2.5. What can go wrong? -- 2.6. Using nsold.m -- 2.7. Examples -- 2.8. Projects -- 2.9. Source code for nsold.m 3. Newton-Krylov methods -- 3.1. Krylov methods for solving linear equations -- 3.2. Computing an approximate Newton step -- 3.3. Preconditioners -- 3.4. What can go wrong? -- 3.5. Using nsoli.m -- 3.6. Examples -- 3.7. Projects -- 4. Broyden's method -- 4.1. Convergence theory -- 4.2. An algorithmis sketch -- 4.3. Computing the Broyden step update -- 4.4. What can go wrong? -- 4.5. Using brsola. m -- 4.6. Examples -- 4.7. Source code for brsola.m.

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"The reader is assumed to have a good understanding of elementary numerical analysis and of numerical linear algebra. Because the examples are so closely coupled to the text, this book cannot be understood without a working knowledge of MATLAB."--Jacket.

Iterative methods (Mathematics)

Newton-Raphson method.

Nonlinear theories.

Iterative methods (Mathematics)

Newton-Raphson method.

Newton-Verfahren

Newton-Verfahren.

Nichtlineare Gleichung

Nichtlineare Gleichung.

Nonlinear theories.

Kelley, C. T.

20201208091906.0

[Book]

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