# Cleve’s Corner: Cleve Moler on Mathematics and ComputingScientific computing, math & more

Posts 21 - 30 of 41

# Perfect Shuffles of Playing Cards

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

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 >>

# Zeroin, Part 1: Dekker’s Algorithm

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 >>

# Dubrulle Creates A Faster Tridiagonal QR Algorithm

Augustin (Austin) Dubrulle deserves to be better known in the numerical linear algebra community. His version of the implicit QR algorithm for computing the eigenvalues of a symmetric tridiagonal matrix that was published in a half-page paper in Numerische Mathematik in 1970 is faster than Wilkinson's version published earlier. It is still a core algorithm in MATLAB today. ... read more >>

# The Ziggurat Random Normal Generator

This is the third in a multi-part series on the MATLAB random number generators. MATLAB has used variants of George Marsaglia's ziggurat algorithm to generate normally distributed random numbers for almost twenty years. ... read more >>

# Parallel Random Number Generators

This is the second of a multi-part series about the MATLAB random number generators. If you ask for help rng, you will get lots of information, including the fact that there are three modern generators.... read more >>

Posts 21 - 30 of 41