Advanced Numerical Methods with Matlab 1: Function Approximation and System Resolution

Content: 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
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s rule5.5. Hermiteâ#x80
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s rule
 5.6. Newtonâ#x80
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CÃt́es rules
 5.7. Gaussâ#x80
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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
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s method
 7.3. Systems with upper triangular matrices
 7.4. Gaussian method
 7.5. Gaussâ#x80
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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
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 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
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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
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n to â#x84
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 A2.3. Optimization without constraints
 Bibliography
 Index
 End User License Agreement.