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Contents
Contents
Ceng 375 Numerical Computations
Cem Özdogan
Date:
28 December 2004
Contents
List of Tables
List of Figures
Introduction to MATLAB
Preliminaries
Analysis vs Numerical Analysis
Computers and Numerical Analysis
An Illustrative Example
Kinds of Errors in Numerical Procedures
Parallel and Distributed Computing
Speed -up and Efficiency
Measuring the Efficiency of Numerical Procedures
Taylor Series
Polynomials
Preliminaries with MATLAB
Solving Nonlinear Equations
Interval Halving (Bisection)
Linear Interpolation Methods
The Secant Method
Linear Interpolation (False Position)
Newton's Method
Complex Roots
Solving Nonlinear Equations with MATLAB I
Muller's Method
Fixed-point Iteration;
Method
Other Rearrangements
Order of Convergence
Multiple Roots
Nonlinear Systems
Solving a System by Iteration
Solving Nonlinear Equations with MATLAB II
Solving Sets of Equations
Matrices and Vectors
Some Special Matrices and Their Properties
Using Computer Algebra Systems
Elimination Methods
Gaussian Elimination
The Gauss-Jordan Method
Using the LU Matrix for Multiple Right-Hand Sides
The Inverse of a Matrix and Matrix Pathology
Pathological Systems
Redundant Systems
Ill-Conditioned Systems
Norms
Matrix Norms
Iterative Methods
Jacobi Method
Gauss-Seidel Iteration
Sparse Matrices and Banded Matrices
Parallel Processing
Solving Sets of Equations with MATLAB
Interpolation and Curve Fitting
Interpolating Polynomials
Fitting a Polynomial to Data
Lagrangian Polynomials
Neville's Method
Divided Differences
Interpolation and Curve Fitting with MATLAB I
Spline Curves
The Equation for a Cubic Spline
Least-Squares Approximations
Nonlinear Data
Least-Squares Polynomials
Use of Orthogonal Polynomials
Interpolation and Curve Fitting with MATLAB II
Approximation of Functions
Chebyshev Polynomials and Chebyshev Series
Chebyshev Polynomials
Economizing a Power Series
Chebyshev Series
Approximation of Functions with MATLAB I
Fourier Series
Fourier Series for Periods Other Than
Fourier Series for Nonperiodic Functions and Half-Range Expansions
Summary
Approximation of Functions with MATLAB II
Numerical Differentiation and Integration
Differentiation with a Computer
Extrapolation Techniques
Numerical Integration - The Trapezoidal Rule
The Trapezoidal Rule
The Composite Trapezoidal Rule
Numerical Differentiation and Integration with MATLAB I
vita
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2004-12-28
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