Pejorative Manifolds of Polynomials and Matrices, part 2

In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold. In case you don't use it in everyday conversation, pejorative means "expressing contempt or disapproval."... read more >>

Pejorative Manifolds of Polynomials and Matrices, part 12

In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold. In case you don't use it in everyday conversation, pejorative means "expressing contempt or disapproval."... read more >>

A Matrix for the New HPL-AI Benchmark2

My colleagues are looking for a matrix to be used in a new benchmark. They've come to the right place.... read more >>

Experiments with Variable Format Half Precision

For the past month I have been working with the variable format 16-bit floating point arithmetic that I described in this post. It has been frustrating work. I have found that the limited precision and limited range of half precision make it barely usable for the kind of experiments with matrix computation that I like to do. In this post I will describe a few of these experiments.... read more >>

Floating Point Arithmetic Before IEEE 7541

In a comment following my post about half-precision arithmetic, "Raj C" asked how the parameters for IEEE Standard 754 floating point arithmetic were chosen. I replied that I didn't know but would try to find out. I called emeritus U. C. Berkeley Professor W. (Velvel) Kahan, who was the principle architect of 754. Here is what I learned.... read more >>

Variable Format Half Precision Floating Point Arithmetic3

A year and a half ago I wrote a post about "half precision" 16-bit floating point arithmetic, Moler on fp16. I followed this with a bug fix, bug in fp16. Both posts were about fp16, defined in IEEE standard 754. This is only one of 15 possible 16-bit formats. In this post I am going to consider all 15.... read more >>

Greg Searle, Fractal Art and Design

If you follow this blog regularly, you know that I love fractals. I recently spent a pleasant afternoon in Nashua, New Hampshire, where my daughter Teresa introduced me to Gregory Searle, a fractal artist and computer geek. Here is his logo.... read more >>

Friday the 13th and the Datetime Method3

Today is Friday, the 13th. In many parts of the world, today is regarded as unlucky. But I want to revisit an old question: is today unlikely? What are the chances that the 13th of any month falls on a Friday? Computing the answer makes use of a new MATLAB® feature, the datetime method.... read more >>