Perfect Shuffles of Playing Cards

Posted by Cleve Moler,

When a deck of playing cards is shuffled perfectly, the result is not random. A perfect shuffle places the cards in a mathematically precise order. As a result, when the most common version of a perfect shuffle is repeated eight times, the deck returns to its original state.... read more >>

Fractal Global Behavior of Newton’s Method

Posted by Cleve Moler,

When the starting point of Newton's method is not close to a zero of the function, the global behavior can appear to be unpredictable. Contour plots of iteration counts to convergence from a region of starting points in the complex plane generate thought-provoking fractal images. Our examples employ the subject of two recent posts, the historic cubic $x^3-2x-5$.... read more >>

John Todd, Savior of Oberwolfach2

Posted by Cleve Moler,

This is the story of how John Todd saved what was to become one of the world's most important research institutions from destruction at the end of World War II.... read more >>

Trip Report: SuperComputing 2015

Posted by Cleve Moler,

SC15, the International Conference for High Performance Computing, Networking, Storage and Analysis, was held in Austin, Texas, last week, November 15 through 20. This is the largest trade show and conference that MathWorks participates in each year.... read more >>

Zeroin, Part 2: Brent’s Version2

Posted by Cleve Moler,

Richard Brent's improvements to Dekker's zeroin algorithm, published in 1971, made it faster, safer in floating point arithmetic, and guaranteed not to fail.... read more >>

Zeroin, Part 1: Dekker’s Algorithm

Posted by Cleve Moler,

Th. J. Dekker's zeroin algorithm from 1969 is one of my favorite algorithms. An elegant technique combining bisection and the secant method for finding a zero of a function of a real variable, it has become fzero in MATLAB today. This is the first of a three part series.... read more >>

Charles Lawson, 1931 – 2015

Posted by Cleve Moler,

Chuck Lawson passed away in July at the age of 83. Chuck was one of the people who introduced me to computing and mathematical software. I worked for him at Caltech's Jet Propulsion Laboratory during the summers of 1961 and 1962, just before and after my first year in grad school.... read more >>

These postings are the author's and don't necessarily represent the opinions of MathWorks.