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 >> ..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 >> ..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 >> ..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 >> ..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 >> ..read more

A few days ago, a bug report from our office in Cambridge caught my attention. Computing the singular values and singular vectors of a particular matrix would sometimes cause MATLAB to crash. Contents Two Computers Math Libraries G3366394 Rank Zero rows Fuzz Flip Now what? Two Computers I use two different two computers regularly. The machine in my home office is a Lenovo ThinkPad® model T14, loaded with two external monitors, several external disc drives, a sound bar and a dedicated internet connection. My traveling machine is a Lenovo ThinkPad X1 Nano with no external hardware. The repo ..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. Contents IBM System/360 Formats Data Hex_ieee ieee2ibm ibm2ieee Examples Comparison Software IBM System/360 The System/360 is a family of mainframe computers that IBM introduced in 1965 and that dom ..read more

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. Contents censusapp2024 Risky Business Splines Exponentials Predictions Conclusion Blogs FMM Software censusapp2024 The latest version of the ce ..read more

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. Contents California Dreaming Closest Pair of Points Pairs DivCon Center Complexity Timing Software References California Dreaming Imagine you are driving a car on the Harbor Freeway in southern California with typical Los Angeles traffic conditions. Among the many things you might want to know is which pair of vehicles is nearest each other. This is an instance of the Closest Pair of Points problem: Given the location of ..read more

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. Contents Why There Wasn't Any Parallel MATLAB Twenty-seven Parallel MATLABs Distributed Computing Toolbox Supercomputing Conference Bill Gates Now There is a Parallel MATLAB Why There Wasn't Any Parallel MATLAB In MATLAB News and Notes for spring 1995, I wrote a one-page Cleve's Corner titled "Why there isn't any parallel MATLAB." There were three reason ..read more