Iterative refinement is a technique introduced by Wilkinson for reducing the roundoff error produced during the solution of simultaneous linear equations. Higher precision arithmetic is required for the calculation of the residuals.... read more >>

This is the second in a series of three posts about the Finite Fourier Transform. This post is about the fast FFT algorithm itself. A recursive divide and conquer algorithm is implemented in an elegant MATLAB function named ffttx.... read more >>

We all use Fourier analysis every day without even knowing it. Cell phones, disc drives, DVDs, and JPEGs all involve fast finite Fourier transforms. This post, which describes touch-tone telephone dialing, is the first of three posts about the computation and interpretation of FFTs. The posts are adapted from chapter 8 of my book, Numerical Computing with MATLAB . ... read more >>

Complex step differentiation is a technique that employs complex arithmetic to obtain the numerical value of the first derivative of a real valued analytic function of a real variable, avoiding the loss of precision inherent in traditional finite differences.... read more >>

The Lambert W function deserves to be better known. It pops up in all sorts of places. And our MATLAB function for evaluating the function is a beautiful use of the Halley method.... read more >>

Chebfun revives a classic video game, with a few mathematical twists (literally)... read more >>

The ROOTS function in Chebfun is one of its most powerful features. This is the second part of my series on Chebfun. Part one is here. ... read more >>

I recently attended "Chebfun and Beyond", a three-day workshop in Oxford, England. Chebfun is a mathematical research and open source software project for numerical computing with functions. I plan to write a series of Cleve's Corner blog posts about Chebfun. ... read more >>

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 >>

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