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 >>

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 coefficient of determination, R-squared or R^2, is a popular statistic that describes how well a regression model fits data. It measures the proportion of variation in data that is predicted by a model. However, that is all that R^2 measures. It is not appropriate for any other use. For example, it does not support extrapolation beyond the domain of the data. It does not suggest that one model is preferable to another.... 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 >>