Numerical Computing with MATLAB

by Cleve Moler.

Book Cover

This is an excellent textbook on basic numerical methods, the MATLAB programming environment, and technical computing. The problems are enjoyable and interesting. I would recommend it highly to anyone who wanted . Note: the entire book, chapter by chapter can be found online here

Here are a few problems from the book I have had time to write the solutions to.

Matlab Code For Various Problems:
    Chapter 7 (Ordinary Differential Equations):
    Chapter 10 (Eigenvalues and Singular Values):
    • prob_10_1.m (a "gallery" of special matrices)
    • prob_10_2.m (the largest and smallest eigenvalue of the magic squares)
    • prob_10_3.m (the eigenvalues of the n-by-n Fourier matrix))
    • prob_10_4.m (the eigenvalues of a differentiation matrix)
    • prob_10_5.m (eigenvalue trajectories)
    • prob_10_6.m (eigenvalue condition numbers)
    • prob_10_7.m (the Rosser matrix)
    • prob_10_8.m (matrices with lambda and 1/lambda as eigenvalues)
    • prob_10_9.m (a timing comparison of three methods for computing the SVD)
    • prob_10_11.m (a graphical comparison of three variants of the QR algorithm)
    • prob_10_13.m (Nikolaus Troje's walker model)
    • prob_10_14.m (diagraphs of various text sources)
    • prob_10_15.m (experiments with the stepsize h in the circle generation solver)
    • ret_mat_A.m (for prob_10_15.m constructs the discrete iteration matrix A)
    • prob_10_16_a.m (Euler's method at generating circles)
    • prob_10_16_b.m (implicit Euler's method at generating circles)
    • prob_10_17.m (compare the numerical predicted aspect ratio to the eigenvector condition number)

John Weatherwax
Last modified: Mon Jul 31 20:43:01 EDT 2006