The twenty-second Householder Symposium on Numerical Linear Algebra is this week, June 8 - June 13, 2025 at Cornell. My talk on Wednesday had the provocative title "A Million-Dollar Matrix". A PDF of the slides available at link_1. The talk covers posts in the Cleve's Corner blog last fall. link_2, link_3, link_4.... read more >>
Two years ago, in March of 2023, an unlikely team of mathematical hobbyists announced the discovery of a remarkable 13-sided polygon that they nick-named the "Hat". Today, a Google search for the Hat's more formal name, "Aperiodic Monotile", yields dozens of links.... read more >>
A look at the structure, and the eigenvalues and singular values of interesting test matrices.... read more >>
Recently, I have made a series of blog posts about Redheffer matrices and the Mertens conjecture. After each of the posts, readers and colleagues offered suggestions to speed up the calculations. Here is a summary of what I have learned.... read more >>
A friend is investigating the use of generative AI in his classes. I asked two different popular chatbots to write MATLAB programs for a mathematically nontrivial problem. Both chatbots understood my query and both wrote plausible MATLAB programs, but one of the programs was not correct. My recommendation for coursework: carefully read and test programs produced by generative AI and repair any incorrect ones.... read more >>
Shortly after I published the second post about the Mertens conjecture, a reader's comment suggested a new approach to computing Redheffer determinants and the Mertens function. It is now possible to compute a half-million values of the Mertens function in about five hours.... read more >>
Shortly after I posted Redheffer, Mertens and One-Million Dollars a few days ago, Mathworks' Pat Quillen made an important observation about computing the Mertens function.... read more >>
I didn't know anything about these topics until a couple of weeks ago. Now I can't stop thinking about them.... read more >>
The NA-Digest is an electronic newsletter for the numerical analysis and scientific software community. The NA-Digest is one of world's first examples of social networking. The Digest is one of the forces that makes our community a living, viable community.... read more >>
Our technical support group recently received a request for a tool that would convert IBM System/360 hexadecimal floating point numbers to the IEEE-754 format. I am probably the only one left at MathWorks that actually used IBM mainframe computers. I thought we had seen the last of hexadecimal arithmetic years ago. But, it turns out that the hexadecimal floating point format is alive and well.... read more >>