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Advanced Numerical Methods with Matlab : Function Approximation and System Resolution.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Newark :
John Wiley & Sons, Incorporated,
2018.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; Table of Contents; Title; Copyright; Preface; PART 1: Introduction; 1 Review of Linear Algebra; 1.1. Vector spaces; 1.2. Linear mappings; 1.3. Matrices; 1.4. Determinants; 1.5. Scalar product; 1.6. Vector norm; 1.7. Matrix eigenvectors and eigenvalues; 1.8. Using Matlab; 2 Numerical Precision; 2.1. Introduction; 2.2. Machine representations of numbers; 2.3. Integers; 2.4. Real numbers; 2.5. Representation errors; 2.6. Determining the best algorithm; 2.7. Using Matlab; PART 2: Approximating Functions; 3 Polynomial Interpolation; 3.1. Introduction; 3.2. Interpolation problems.
- 3.3. Polynomial interpolation techniques3.4. Interpolation with the Lagrange basis; 3.5. Interpolation with the Newton basis; 3.6. Interpolation using spline functions; 3.7. Using Matlab; 4 Numerical Differentiation; 4.1. First-order numerical derivatives and the truncation error; 4.2. Higher-order numerical derivatives; 4.3. Numerical derivatives and interpolation; 4.4. Studying the differentiation error; 4.5. Richardson extrapolation; 4.6. Application to the heat equation; 4.7. Using Matlab; 5 Numerical Integration; 5.1. Introduction; 5.2. Rectangle method; 5.3. Trapezoidal rule.
- 5.4. Simpsonâ#x80;#x99;s rule5.5. Hermiteâ#x80;#x99;s rule; 5.6. Newtonâ#x80;#x93;CÃt́es rules; 5.7. Gaussâ#x80;#x93;Legendre method; 5.8. Using Matlab; PART 3: Solving Linear Systems; 6 Matrix Norm and Conditioning; 6.1. Introduction; 6.2. Matrix norm; 6.3. Condition number of a matrix; 6.4. Preconditioning; 6.5. Using Matlab; 7 Direct Methods; 7.1. Introduction; 7.2. Method of determinants or Cramerâ#x80;#x99;s method; 7.3. Systems with upper triangular matrices; 7.4. Gaussian method; 7.5. Gaussâ#x80;#x93;Jordan method; 7.6. LU decomposition; 7.7. Thomas algorithm; 7.8. Cholesky decomposition; 7.9. Using Matlab; 8 Iterative Methods.
- 8.1. Introduction8.2. Classical iterative techniques; 8.3. Convergence of iterative methods; 8.4. Conjugate gradient method; 8.5. Using Matlab; 9 Numerical Methods for Computing Eigenvalues and Eigenvectors; 9.1. Introduction; 9.2. Computing det (A â#x88;#x92; λI) directly; 9.3. Krylov methods; 9.4. LeVerrier method; 9.5. Jacobi method; 9.6. Power iteration method; 9.7. Inverse power method; 9.8. Givensâ#x80;#x93;Householder method; 9.9. Using Matlab; 10 Least-squares Approximation; 10.1. Introduction; 10.2. Analytic formulation; 10.3. Algebraic formulation.
- 10.4. Numerically solving linear equations by QR factorization10.5. Applications; 10.6. Using Matlab; PART 4: Appendices; Appendix 1: Introduction to Matlab; A1.1. Introduction; A1.2. Starting up Matlab; A1.3. Mathematical functions; A1.4. Operators and programming with Matlab; A1.5. Writing a Matlab script; A1.6. Generating figures with Matlab; Appendix 2: Introduction to Optimization; A2.1. Introduction; A2.2. Standard results on functions from â#x84;#x9D;n to â#x84;#x9D;; A2.3. Optimization without constraints; Bibliography; Index; End User License Agreement.