This is the first of a multi-part series about the MATLAB random number generators.... 続きを読む >>

My experience with the forthcoming MATLAB watch exceeds my most optimistic expectations. The watch has not yet been announced officially, but a few of us have been testing prototypes for the past several weeks.... 続きを読む >>

I came across this "ornamental geometric inequality" in a tribute to Lothar Collatz.... 続きを読む >>

Single and double precision are combined to facilitate a triple precision accumulated inner product.... 続きを読む >>

Iterative refinement is a technique introduced by Wilkinson for reducing the roundoff error produced during the solution of simultaneous linear equations. Higher precision arithmetic is required for the calculation of the residuals.... 続きを読む >>

Steve Eddins has recently posted a series in his blog about colormaps. I want to add one more post. With release R2014b, we are retiring jet as the default colormap, after many years of faithful service. But did you ever wonder where jet originated, and how it came to be the default? And did you ever come across colormaps like pink and bone?... 続きを読む >>

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 that no matter what value of $n$ is chosen to start, the process eventually terminates at $n=1$. Do not expect a proof, or a counterexample, in this blog. ... 続きを読む >>

The prime spiral was discovered by Stanislaw Ulam in 1963, and featured on the cover of Scientific American in March, 1964. ... 続きを読む >>

Season's Greetings, 2014 help greetings % greetings Seasonal holiday fractal. % greetings(phi) generates a seasonal holiday fractal that depends % upon the parameter phi. The default... 続きを読む >>

An incredible book, published in several editions from 1909 to 1933, by German mathematicians Eugene Jahnke and Fritz Emde, contains definitions and formulas for mathematical functions, hand-calculated tables of function values, and meticulous hand-drawn 2- and 3-dimensional graphs. An English edition was published by Dover in 1945.... 続きを読む >>