This file is the
table of contents for lectures notes prepared by Moody Chu for the courses
MA428/MA580 and MA427/MA7800.
chapter 1. Error Analysis
o
Measurement
of Errors
o
Representation
of Numbers
o
Stability
and Conditioning
Chapter 2. System of Linear Equations --- Direct Approach
o
General
Consideration
o
Gaussian
Elimination
o
Mathematical
Pivoting
o
Error
Analysis
o
Orthogonal
Decomposition
Chapter 3. System of Linear Equations --- Iterative Approach
o
General
Consideration
o
Relaxation
Methods
o
Acceleration
Methods
o
Conjugate
Gradient Methods
o
GMRES
Chapter 4. Least Squares Problem
o
Linear
Least Squares Problems
o
Singular
Value Decomposition
Chapter 5. Algebraic Eigenvalue Problems
o
Location
and Perturbation Results
o
Power
Methods and Inverse Power Methods
o
QR
Algorithm
Chapter 6. System of Nonlinear Equations
o
Theory
of Newton-Raphson Method
o
The Broyden Method
o
Sturm
Sequence
o
Methods
for Polynomials
Chapter 7. Approximation Theory
o
Lagrangian
Interpolation Formula
o
Newton's
Interpolation Formula
o
Osculatory
Interpolation
o
Spline
Interpolation
o
Trigonometric
Interpolation
o
Fast
Fourier Transform
Chapter 8. Differentiation and Integration
o
Numerical
Differentiation
o
Richardson
Extrapolation
o
Newton-Cotes
Quadrature
o
Gaussian
Quadrature
o
Weight
Functions and Special Integrals
o
Adaptive
Integration
Chapter 9. Numerical Ordinary Differential Equations -
Initial Value Problems
o
Linear
Multi-step Methods
o
Stability
Theory of Multi-step Methods
o
Predictor
and Corrector Methods
o
Runge-Kutta Methods
Chapter 10. Numerical Ordinary Differential Equations –
Boundary Value Problems
o
Ordinary
Shooting Method --- An Example
o
Multiple
Shooting Methods --- The Set-up
o
Solving
Nonlinear Equations --- Homotopy Method
o
Finite
Difference Method
o
Finite
Element Methods