I first encountered the Hilbert matrix when I was doing individual studies under Professor John Todd at Caltech in 1960. It has been part of my professional life ever since.... 続きを読む >>

The floating point arithmetic format that occupies 128 bits of storage is known as binary128 or quadruple precision. This blog post describes an implementation of quadruple precision programmed entirely in the MATLAB language.... 続きを読む >>

A MATLAB object for arithmetic with Roman numerals provides an example of object oriented programming. I had originally intended this as my April Fools post, but I got fascinated and decided to make it the subject of a legitimate article.... 続きを読む >>

I've long known that my Erdös Number is 3. This means that the length of the path on the graph of academic coauthorship between me and mathematician Paul Erdös is 3. Somewhat to my surprise, I recently discovered that I can also trace a chain of coauthorship to Donald J. Trump. My Trump number is 5.... 続きを読む >>

A binary tree is an elegant way to represent and process Morse code. The new MATLAB graph object provides an elegant way to manipulate binary trees. A new app, morse_tree, based on this approach, is now available in version 2.40 of Cleve's Laboratory.... 続きを読む >>

The adjacency matrix of a hypercube demonstrates the new MATLAB graph object.... 続きを読む >>

MIT's Professor Daniel Frey recently introduced me to an ancient mechanical puzzle known as "Chinese Rings", "Patience", or "Baguenaudier." I have modified Daniel's simulator to produce a new app. The state space of the puzzle forms a hypercube.... 続きを読む >>

"ULP" stands for "unit in the last place." An ulps plot samples a fundamental math function such as $\sin{x}$, or a more esoteric function like a Bessel function. The samples are compared with more accurate values obtained from a higher precision computation. A plot of the accuracy, measured in ulps, reveals valuable information about the underlying algorithms.... 続きを読む >>

A headline in the New York Times at the end of 2016 said "Growth of U.S. Population Is at Slowest Pace Since 1937". This prompted me to revisit an old chestnut about fitting and extrapolating census data. In the process I have added a couple of nonlinear fits, namely the logistic curve and the double exponential Gompertz model.... 続きを読む >>

When I was in high school in the 1950's, I didn't know anything about matrices. But I nearly encountered one when I wrote a paper for my physics class about the color scheme that allowed new color TV broadcasts to be compatible with existing black-and-white TV receivers.... 続きを読む >>