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.... 続きを読む >>

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.... 続きを読む >>

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.... 続きを読む >>

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.... 続きを読む >>

I didn't know anything about these topics until a couple of weeks ago. Now I can't stop thinking about them.... 続きを読む >>

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.... 続きを読む >>

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.... 続きを読む >>

The graphics in my post about R^2 were produced by an updated version of a sixty-year old program involving the U.S. census. Originally, the program was based on census data from 1900 to 1960 and sought to predict the population in 1970. The software back then was written in Fortran, the predominate technical programming language a half century ago. I have updated the MATLAB version of the program so that it now uses census data from 1900 to 2020.... 続きを読む >>

The Closest Pair of Points problem is a standard topic in an algorithms course today, but when I taught such a course fifty years ago, the algorithm was not yet known.... 続きを読む >>

I have just returned from the MathWorks company meeting celebrating our 40th Anniversary. In one of the presentations, Jos Martin described how Parallel MATLAB was introduced almost twenty years ago. Here are a few slides from Jos's talk.... 続きを読む >>