A couple of questions in comments on recent blog posts have prompted me to discuss matrix condition numbers.... read more >>

The Householder meetings on Numerical Linear Algebra have been held roughly every three years since 1961. The twentieth, with the logo HHXX, was held June 18th through 23rd at Virginia Tech in Blacksburg, Virginia. I've been to 17 of the meetings. They have been an important part of my professional life and I've written Cleve's Corner articles and blog posts about them, MathWorks News & Notes, and Householder XIX.... read more >>

The floating point arithmetic format that occupies 128 bits of storage is known as binary128 or quadruple precision. This blog post describes an implementation of quadruple precision programmed entirely in the MATLAB language.... read more >>

The floating point arithmetic format that requires only 16 bits of storage is becoming increasingly popular. Also known as half precision or binary16, the format is useful when memory is a scarce resource.... read more >>

A report about a possible bug in format bank and a visit to a local hardware store made me realize that doing decimal arithmetic with binary floating point numbers is like tightening a European bolt with an American socket wrench.... read more >>

"ULP" stands for "unit in the last place." An ulps plot samples a fundamental math function such as $\sin{x}$, or a more esoteric function like a Bessel function. The samples are compared with more accurate values obtained from a higher precision computation. A plot of the accuracy, measured in ulps, reveals valuable information about the underlying algorithms.... read more >>

A headline in the New York Times at the end of 2016 said "Growth of U.S. Population Is at Slowest Pace Since 1937". This prompted me to revisit an old chestnut about fitting and extrapolating census data. In the process I have added a couple of nonlinear fits, namely the logistic curve and the double exponential Gompertz model.... read more >>

My favorite ordinary differential equation provides a good test of ODE solvers, both numeric and symbolic. It also provides a nice illustration of the underlying existence theory and error analysis.... read more >>

I am launching a project that I call Cleve's Laboratory. My most recent Cleve's Corner column in MathWorks News & Notes is about the project. The MATLAB app itself is available for download from the MATLAB Central File Exchange.... read more >>

This is a follow-up to my previous follow-up, posted several days ago. A very careful reader, Bruno Bazzano, contributed a comment pointing out what he called "a small typo" in my code for the classic Gram-Schmidt algorithm. It is more than a small typo, it is a serious blunder. I must correct the code, then do more careful experiments and reword my conclusions.... read more >>