# The Three n Plus One Conjecture2

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. ... read more >>

# Prime Spiral2

The prime spiral was discovered by Stanislaw Ulam in 1963, and featured on the cover of Scientific American in March, 1964. ... read more >>

# Season’s Greetings, 20142

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 value of phi is the golden ratio. % What happens for other values of phi? Try both simple... read more >>

# Touch-Tone Telephone Dialing8

We all use Fourier analysis every day without even knowing it. Cell phones, disc drives, DVDs, and JPEGs all involve fast finite Fourier transforms. This post, which describes touch-tone telephone dialing, is the first of three posts about the computation and interpretation of FFTs. The posts are adapted from chapter 8 of my book, Numerical Computing with MATLAB . ... read more >>

# Householder Symposium XIX Trip Report

The nineteenth Householder Symposium, Householder XIX, was held June 8-13 at Sol Cress, a conference center near Spa, Belgium. If you have been following either the web or the newletter edition of Cleve's Corner you know that the Gatlinburg/Householder series of conferences have played an important role in both my professional life and the history of MATLAB. I attended what turned out to be the third conference in the series, in Gatlinburg, Tennesse, when I was a graduate student in 1964. I have been to all 17 of the conferences that have been held since 1964. Here is a link to my News and Notes article about the Gatlinburg/Householder conferences.... read more >>

# Singular Value Analysis of Cryptograms

The Singular Value Decomposition of the digram frequency matrix of a text coded with a simple substitution cypher can reveal information about the vowels and consonants in the text. ... read more >>

# Reverse Singular Value Decomposition2

Employing a factorization based on the least significant singular values provides a matrix approximation with many surprisingly useful properties. This Reverse Singular Value Decomposition, RSVD, is also referred to as Subordinate Component Analysis, SCA, to distinguish it from Principal Component Analysis. ... read more >>

# Higher Resolution Penny

High resolution measurements of the depth of the mold for the United States one cent coin provide an interesting data set.... read more >>

# Music, Sparse Matrices, and London Billboards2

At the recent SIAM conference on Parallel Processing for Scientific Computing, I met my friend Tim Davis. Tim is a professor at the University of Florida, a consultant to MathWorks, and author of many of the functions involved in MATLAB sparse matrix calculations. One of his hobbies involves... read more >>

# The Tektronix 40812

The Tektronix 4081 minicomputer at Argonne National Laboratory in the summers of 1977 and '78 played an important role in the early development of MATLAB.... read more >>