How do you compute the hypotenuse of a right triangle without squaring the lengths of the sides and without taking any square roots?... 続きを読む >>

I have been interested in the computation of the matrix exponential, $e^A$, for a long time. A recent query from a user provides a provocative example.... 続きを読む >>

MATLAB has two different functions for piecewise cubic interpolation, spline and pchip. Why are there two? How do they compare? ... 続きを読む >>

We all know that Friday the 13th is unlucky, but is it unlikely?... 続きを読む >>

An esoteric fact about matrices is that any real matrix can be written as the product of two symmetric matrices. I've known about this fact for years, but never seriously explored the computational aspects. So I'm using this post to clarify my own understanding of what I'll call the symmetric pair decomposition. It turns out that there are open questions. I don't think we know how to reliably compute the factors. But I also have to admit that, even if we could compute them, I don't know of any practical use.... 続きを読む >>