Denormal floating point numbers and gradual underflow are an underappreciated feature of the IEEE floating point standard. Double precision denormals are so tiny that they are rarely numerically significant, but single precision denormals can be in the range where they affect some otherwise unremarkable computations. Historically, gradual underflow proved to be very controversial during the committee deliberations that developed the standard. ... 続きを読む >>

This is the first part of a two-part series about the single- and double precision floating point numbers that MATLAB uses for almost all of its arithmetic operations. (This post is adapted from section 1.7 of my book Numerical Computing with MATLAB, published by MathWorks and SIAM.) ... 続きを読む >>

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.... 続きを読む >>

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. ... 続きを読む >>

High resolution measurements of the depth of the mold for the United States one cent coin provide an interesting data set.... 続きを読む >>

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.... 続きを読む >>

I am surprised when many of the singular values of a nonsymmetric variant of the Hilbert matrix turn out to be nearly equal to $\pi$. The explanation involves the Fourier series for a square wave.... 続きを読む >>

The Rosser matrix is a classic matrix eigenvalue test problem.... 続きを読む >>

Even though I am one of the founders of the MathWorks, I only acted as an advisor to the company for its first five years. During that time, from 1985 to 1989, I was trying my luck with two Silicon Valley computer startup companies. Both enterprises failed as businesses, but the experience taught me a great deal about the computer industry, and influenced how I viewed the eventual development of MATLAB. The second startup was known as Ardent Computer for most of its brief existence.... 続きを読む >>

Even though I am one of the founders of the MathWorks, I only acted as an advisor to the company for its first five years. During that time, from 1985 to 1989, I was trying my luck with two Silicon Valley computer startup companies. Both enterprises failed as businesses, but the experience taught me a great deal about the computer industry, and influenced how I viewed the eventual development of MATLAB. The second startup was known as Ardent Computer for most of its brief existence. We built a machine known as the Titan.... 続きを読む >>