How can you measure the distance between two words? How can you find the closest match to a word in a list of words? The Levenshtein distance between two strings is the number of single character deletions, insertions, or substitutions required to transform one string into the other. This is also known as the edit distance.... 続きを読む >>

The Householder meetings on Numerical Linear Algebra have been held roughly every three years since 1961. The twentieth, with the logo HHXX, was held June 18th through 23rd at Virginia Tech in Blacksburg, Virginia. I've been to 17 of the meetings. They have been an important part of my professional life and I've written Cleve's Corner articles and blog posts about them, MathWorks News & Notes, and Householder XIX.... 続きを読む >>

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 >>