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Random Number Generators, Mersenne Twister
This is the first of a multi-part series about the MATLAB random number generators....

11 years ago

Published

Experiencing the MATLAB Watch
My experience with the forthcoming MATLAB watch exceeds my most optimistic expectations. The watch has not yet been...

11 years ago

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An Ornamental Geometric Inequality
I came across this "ornamental geometric inequality" in a tribute to Lothar Collatz....

11 years ago

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Triple Precision Accumlated Inner Product
Single and double precision are combined to facilitate a triple precision accumulated inner product....

11 years ago

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Iterative Refinement for Solutions to Linear Systems
Iterative refinement is a technique introduced by Wilkinson for reducing the roundoff error produced during the solution of...

11 years ago

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Origins of Colormaps
Steve Eddins has recently posted a series in his blog about colormaps. I want to add one more post. With release R2014b, we...

11 years ago

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The Three n Plus One Conjecture
If $n$ is odd, replace $n$ by $3n+1$, if not, replace $n$ by $n/2$. Repeat. A famous conjecture made by Lothar Collatz is...

11 years ago

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Prime Spiral
The prime spiral was discovered by Stanislaw Ulam in 1963, and featured on the cover of Scientific American in March,...

11 years ago

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Season’s Greetings, 2014
Season's Greetings, 2014 help greetings % greetings Seasonal holiday fractal. % greetings(phi) generates a...

11 years ago

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Jahnke and Emde, Revisited
An incredible book, published in several editions from 1909 to 1933, by German mathematicians Eugene Jahnke and Fritz Emde,...

11 years ago

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MathWorks Logo, Part Five, Evolution of the Logo
Our plots of the first eigenfunction of the L-shaped membrane have changed several times over the last fifty years.... read...

11 years ago

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MathWorks Logo, Part Four, Method of Particular Solutions Generates the Logo
The Method of Particular Solutions computes a highly accurate approximation to the eigenvalue we have been seeking, and...

11 years ago

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MathWorks Logo, Part Three, PDE Toolbox
The Partial Differential Equation Toolbox contains tools for the analysis of PDEs in two space dimensions and time. It is...

11 years ago

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MathWorks Logo, Part Two. Finite Differences
After reviewing the state of affairs fifty years ago, I use classic finite difference methods, followed by extrapolation, to...

11 years ago

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MathWorks Logo, Part One. Why Is It L Shaped?
MathWorks is the only company in the world whose logo satisfies a partial differential equation. Why is the region for this...

11 years ago

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Finite Fourier Transform Matrix
This is the third in a series of posts on the finite Fourier transform. The Fourier matrix produces an interesting graphic...

11 years ago

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FFT, Fast Finite Fourier Transform
This is the second in a series of three posts about the Finite Fourier Transform. This post is about the fast FFT algorithm...

11 years ago

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Touch-Tone Telephone Dialing
We all use Fourier analysis every day without even knowing it. Cell phones, disc drives, DVDs, and JPEGs all involve fast...

11 years ago

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Complete Pivoting and Hadamard Matrices
For several years we thought Hadamard matrices showed maximum element growth for Gaussian elimination with complete...

11 years ago

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Gaussian Elimination with Partial Pivoting
In rare cases, Gaussian elimination with partial pivoting is unstable. But the situations are so unlikely that we continue...

11 years ago

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Floating Point Denormals, Insignificant But Controversial
Denormal floating point numbers and gradual underflow are an underappreciated feature of the IEEE floating point standard....

11 years ago

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Floating Point Numbers
This is the first part of a two-part series about the single- and double precision floating point numbers that MATLAB uses...

11 years ago

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Householder Symposium XIX Trip Report
The nineteenth Householder Symposium, Householder XIX, was held June 8-13 at Sol Cress, a conference center near Spa,...

11 years ago

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Ordinary Differential Equations, Stiffness
Stiffness is a subtle concept that plays an important role in assessing the effectiveness of numerical methods for ordinary...

11 years ago

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Ordinary Differential Equation Solvers ODE23 and ODE45
The functions ode23 and ode45 are the principal MATLAB and Simulink tools for solving nonstiff ordinary differential...

11 years ago

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Ordinary Differential Equation Suite
MATLAB and Simulink have a powerful suite of routines for the numerical solution of ordinary differential equations. ...

11 years ago

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Periodic Solutions to the Lorenz Equations
Changing the value of a parameter in the equations that produce the famous Lorenz chaotic attractor yields nonlinear...

11 years ago

Published

Singular Value Analysis of Cryptograms
The Singular Value Decomposition of the digram frequency matrix of a text coded with a simple substitution cypher can reveal...

12 years ago

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Reverse Singular Value Decomposition
Employing a factorization based on the least significant singular values provides a matrix approximation with many...

12 years ago

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Higher Resolution Penny
High resolution measurements of the depth of the mold for the United States one cent coin provide an interesting data...

12 years ago