ncm

ncm, an Octave code which accompanies the textbook "Numerical Computing with MATLAB", by Cleve Moler, and illustrates algorithms for the 3n+1 problem, blackjack, eigenvalue computations, fast Fourier transforms, Fibonacci numbers, file encryption, the flame differential equation, the fractal fern, the Lorenz differential equation, a membrane partial differential equation, minimization of a scalar function, ordinary differential equations, the pendulum differential equation, piecewise cubic Hermite interpolation, polynomial interpolation, quadrature for approximate integration, random number generation, tridiagonal linear system solution, the singular value decomposition, solution of a nonlinear equation.

The textbook includes chapters on the following topics:

Introduction to MATLAB;
Linear Equations;
Interpolation;
Zeros and Roots;
Least Squares;
Quadrature;
Ordinary Differential Equations;
Fourier Analysis;
Random Numbers;
Eigenvalues and Singular Values;
Partial Differential Equations;

Licensing:

Languages:

ncm is available in a MATLAB version and an Octave version

Author:

Cleve Moler.

Related Data and Programs:

ncm_test

exm, an Octave code which illustrates the computational experiments in "Experiments with Matlab", by Cleve Moler.

Reference:

Cleve Moler,
Numerical Computing with MATLAB,
SIAM, 2004,
ISBN13: 978-0-898716-60-3,
LC: QA297.M625,
ebook: https://www.mathworks.com/moler/chapters.html
Cleve Moler,
Experiments with MATLAB,
ebook: https://www.mathworks.com/moler/exm/index.html

Source Code:

bigscreen.m, set graphics properties for large audiences.
bizcard.m, Future version of The MathWorks business card..
blackjack.m, simulates the game of blackjack.
brownian.m, two-dimensional random walk.
bslashtx.m, solve a linear system (emulates the MATLAB backslash operator).
censusgui.m, try to predict the US population in the year 2010.
circlegen.m, generate approximate circles.
crypto.m, cryptography example.
digraph_ncm.m, principal component analysis of text digraph frequency matrix.
eigshow.m, graphical demonstration of eigenvalues and singular values.
eigsvdgui.m, demonstrate computation of matrix eigenvalues and singular values.
encrypt.m, apply the CRYPTO function to a text file.
fern.m, the fractal fern.
fftgui.m, demonstrate finite Fourier transform.
fftmatrix.m, plot columns of the finite Fourier transform matrix.
ffttx.m, textbook implementation of the fast finite Fourier transform.
fibnum.m, generates the n-th Fibonacci number.
fibonacci.m, the Fibonacci sequence.
finitefern.m, the Fractal fern.
flame.m, a stiff ordinary differential equation.
floatgui.m, show the structure of floating point numbers.
fmintx.m, textbook version of fminbd, minimization with bound constraints.
font.m, command window font size.
fzerogui.m, demonstrate the zero finding algorithm used by FZERO.
fzerotx.m, textbook version of the zero finding algorithm FZERO.
goldfract.m, golden ratio continued fraction.
golub.m, badly conditioned integer test matrices.
greetings.m, seasonal holiday fractal.
humps.m, a test function with two humps.
imagesvd.m, principal component analysis of monochrome and color images.
inregion.m, True for points inside or on a polygonal region.
interp2dgui.m, behavior of periodic parametric curves.
interpgui.m, behavior of interpolating functions.
is_octave.m, is TRUE if the code is being run by Octave.
lorenzgui.m, plot the orbit around the Lorenz chaotic attractor.
lugui.m, Gaussian elimination demonstration.
lutx.m, triangular factorization, textbook version.
membranetx.m, textbook version of code to compute eigenfunctions of a membrane.
ncmgui.m, master GUI for Numerical Computing with MATLAB..
ncmlogo.m, NCM logo, the L-shaped membrane.
ode23tx.m, solve non-stiff differential equations.
pagerank.m, Google's pagerank.
pagerankpow.m, pagerank by the power method.
pchiptx.m, textbook piecewise cubic Hermite iterpolation.
pdegui.m, demonstrates the solution of model partial differential equations (PDE's) using the finite difference method (FDM). The PDE's include the Poisson equation, the time dependent heat equation, the wave equation, and an eigenvalue problem. The domains include the square, the L-region, the H-region, a disc, an annulus, a heart, two "drums", and a hand.
pennymelt.m, heat a penny.
piecelin.m, piecewise linear interpolation.
pivotgolf.m, pivot pickin' golf.
polyinterp.m, polynomial interpolation.
powersin.m, power series for sin(x).
primespiral.m, Ulam's prime number spiral.
qrsteps.m, orthogonal triangular decomposition.
quadgui.m, numerical evaluation of a definite integral.
quadtx.m, evaluate definite integral numerically.
randgui.m, Monte Carlo computation of pi.
randmcg.m, multiplicative congruential uniform random number generator.
randncond.m, condition of random matrices.
randntx.m, textbook version of randn.
randssp.m, multiplicative congruential uniform random number generator based on IBM SSP.
randtx.m, obsolete random number generator.
rungeinterp.m, Runge's polynomial interpolation example.
splinetx.m, textbook spline function.
stegano.m, investigate steganography in the default image.
surfer.m, create the adjacency graph of a portion of the web.
swinger.m, the double pendulum.
swingernew.m, new version of the double pendulum code.
threenplus1.m, the 3n+1 or Collatz problem.
touchtone.m, Use FFT to synthesize and analyze telephone dialing
tridisolve.m, Solve tridiagonal system of equations.

Last revised on 02 July 2023.