README.md

Numerical Analysis: Theory and Experiments
Brian Sutton

Numerical Analysis: Theory and Experiments is a textbook on numerical analysis. Numerical methods are designed and implemented, and then they are analyzed through a combination of mathematical theory and numerical experimentation. Problem areas include interpolation, integration, linear systems, zero finding, and differential equations. Chebyshev methods are used early and often.

This package is a library of numerical routines that accompany the book.

MATLAB versus Octave

The original package contains MATLAB codes. This is a port to Octave.

Installation

The library is installed as follows:

1. Download the package nate-octave.tar.gz.
2. Start Octave.
3. Install the package:

   octave> pkg install nate-octave.tar.gz
   

   The full pathname must be provided if nate-octave.tar.gz is not located in the current working directory.
4. Load the package:

   octave> pkg load nate-octave
   

5. Verify that the library routines are available as follows:

   octave> nate
   Numerical Analysis: Theory and Experiments
   

6. Set the numeric format to long:

   octave> format long
   

Steps 4-6 must be repeated each time Octave is restarted.

Demonstration

The following code computes and plots the arctan function.

>> g = @(x) 1/(1+x^2); a = 0; b = 10;
>> fa = 0;
>> qs = samplecheb(g,[a b],60);
>> ps = antiderivcheb(fa,qs,[a b]);
>> p = interpcheb(ps,[a b]);
>> newfig;
>> plotfun(p,[a b],'displayname','p');
>> ylim([0 pi/2]);
>> legend('location','southeast');