Pythagorean Addition 1

Posted by Cleve Moler,

How do you compute the hypotenuse of a right triangle without squaring the lengths of the sides and without taking any square roots?... read more >>

Splines and Pchips 2

Posted by Cleve Moler,

MATLAB has two different functions for piecewise cubic interpolation, spline and pchip. Why are there two? How do they compare?... read more >>

Symmetric Pair Decomposition 1

Posted by Cleve Moler,

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.... read more >>