I am very excited to incorporate sound in animations. This blog post has five examples with links to videos enclosed in '+ + + +'.... 続きを読む >>

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 >>

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.... 続きを読む >>

Floating point arithmetic doesn't get the respect it deserves. Many people consider it mysterious, fuzzy, unpredictable. These misgivings often occur in discussion of vector sums. Our provocatively named SuperSum is intended to calm these fears.... 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 >>