Genetic Algorithms Basics
An introduction to conventional genetic algorithms.
An excerpt from Carl Sagan's "Cosmos".
Picture of a Heike crab that was referred to in Carl Sagan's "Cosmos".
Japanese paintings depicting the sea battle at Danno-ura in the Japanese Inland Sea on April 24, 1185.
The Differential Evolution homepage.
Optimization using Storn's Differential Evolution algorithm.
Script to use the Golden Section method to find the minimum of a function in one-dimension. Script is written specially for example 6.8 in the textbook.
A function to compute the value of the function used in example 6.8 in the above script.
A function using the Golden Section method to find the minimum of a function in one-dimension.
A function using the steepest descent method for multi-parameter optimization. Line search using the Armijo method is implemented.
A function to compute the Rosenbrock function (needed for the steepest descent method).
A function to compute the gradient of the Rosenbrock function (needed for the steepest descent method).
An implementation of a version of Storn's Differential Evolution algorithm.
Script file to run the above Differential Evolution program.
The Griewangk function used in the above script.
Script file to plot the Griewangk function in one-dimension.
Interpolation using Monomial Basis Functions
Divided Difference (a better implementation)
Horner's Method for evaluating polynomials
A dumb way to evaluate polynomials
An even dumber way to evaluate polynomials
Horner's Method for evaluating polynomials with a shift
Problem interpolating a noisy straight line using polynomials
Problem with interpolation using a single polynomial of high degree
Interpolation using Rational Function
Interpolation using Rational Function (improved implementation)
Testing Rational Function interpolation
Matlab Function for Natural Cubic Spline
Another example of the Natural Cubic Spline
An example using Parametric Cubic Spline
A second example using Parametric Natural Cubic Spline
A third example using Parametric Cubic Spline
Divided Differences method to construct Newton's interpolant.
Rational Function interpolation.
Interpolation using the cubic spline.
Interpolation using parametric cubic spline.
Script to test various quadrature rules
8-Point Gauss-Legendre Quadrature
24-Point Gauss-Legendre Quadrature
48-Point Gauss-Legendre Quadrature
Adaptive quadrature based on Simpson's rule
Adaptive quadrature based on the Gauss-Legendre Quadrature rule
Forward Difference Formula for the first derivative
Richardson Extrapolation to accelerate the computation of Pi according to Archemedes
Script to test Romberg quadrature
A problematic function used to test various quadrature rules
A function used to test various quadrature rules
A chapter from Prof. Cleve Moler's book: "Numerical Computing with Matlab" - using the FFT to study the Dual Tone Multi-Frequency system used in touch-tone phones, and to study sun-spots activities for the past 300 years.
You can use the program to explore the use of the FFT to study the Dual Tone Multi-Frequency system. This program needs to read in data from the following binary file. Please save this file in the same directory as the above Matlab program.
The Matlab GUI program allows you to explore various aspects of the DFT.
A Matlab program showing some of Matlab's sound processing capabilities.
To run the above program, you will need the Matlab program as well as the following 2 sound data files: fh.wav whistle.wav.
Eigenvalues and eigenvectors: What do they all mean.
A physical example using Java animation to elucidate the meaning of eigenvalues and eigenvectors.
Using power iteration to compute the dominant eigenvalue and its corresponding eigenvector.
A function using normalized power iteration to compute the dominant eigenvalue and its corresponding eigenvector.
script to use the above function.
A function using inverse iteration to compute the least dominant eigenvalue and its corresponding eigenvector.
script to use the above function.
Using shifted inverse iteration to compute any eigenvalue and its corresponding eigenvector.
A function using power iteration and Rayleigh quotient to compute the dominant eigenvalue and its corresponding eigenvector.
A script to call and run the above function to compute the dominant eigenvalue and its corresponding eigenvector using power iteration and Rayleigh quotient.
A function implementing QR iteration to compute the eigenvalues.
script to compute the eigenvalues of a matrix using QR iteration.
Introduction to Steganography. Illustrate how images can be embedded in the least-significant bits of seemingly harmless image.
A Matlab program for the above example.
Illustration of matrices defined over a finite field, handling of character set and strings using the "Hill Cipher".
A Matlab function implementing the above example.
A Matlab function utilizing the above function to encrypt the text in a given text file.
Lecture notes on the use of sparse matrices in Matlab.
Matlab program illustrating the use of sparse matrices.
An example to study the Bucky balls.
