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Numerical Analysis - Table of Contents
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Overview
Overview
Preface
Table of Contents
About Author(s)
Products
Offering: Numerical Analysis
Titles: Numerical Analysis
By Dr. Indy Lagu
1. Examples and Prospectus
1.1 - Introduction
2. Solution of Non-Linear Equations
2.1 - Taylor's Theorem
2.2 - Bisection Method
2.3 - Regula-Falsi
2.4 - Fixed Point Iteration
2.5 - Speed of Convergence
2.6 - Aitken Acceleration
2.7 - Steffensen's Method
2.8 - Newton's Method
2.9 - The Secant Method
3. Numerical Linear Algebra
3.1 - LU Decomposition
3.2 - Conditioning
3.3 - Pivoting Strategies
3.4 - Iterative Improvement
3.5 - Special Matrices
3.6 - Diagonally Dominant Matrices
3.7 - Positive Definite Matrices
3.8 - Iterative Methods for Linear Systems
3.9 - Jacobi's Method
3.10 - Gauss-Seidel
3.11 - Successive Over Relaxation
3.12 - Eigenvalues and Eigenvectors
3.13 - Stability of Eigenvectors
3.14 - The Power Method
3.15 - Deflation
3.16 - Inverse Power Method
3.17 - The QR Algorithm
4. Non-Linear Equations in Several Variables
4.1 - Hademard's Lemma
4.2 - Fixed Point Iteration in n-Dimensional Euclidean Space
4.3 - Multivariate Newton's Method
4.4 - Multivariate Secant Method
4.5 - Broyden's Method
4.6 - Newton-SOR
5. Interpolation and Approximation
5.1 - Introduction
5.2 - Lagrange Interpolation
5.3 - Newton Interpolation and Divided Differences
5.4 - Error Formula
5.5 - Runge's Example
5.6 - Tchebycheff Polynomials
5.7 - Splines
5.8 - Least Squares
5.9 - Least Squares Splines
5.10 - Fast Fourier Transformation
6. Numerical Integration
6.1 - Trapezoid Rule
6.2 - Simpson's Rule
6.3 - Romberg Integration
7. Differential Equations
7.1 - Euler's Method
7.2 - Higher Order Taylor Methods
7.3 - Second Order Runge-Kutta
7.4 - Fourth Order Runge-Kutta