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Numerical Analysis - Table of Contents

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