# Iterative Refinement for Solutions to Linear Systems4

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 >>

# FFT, Fast Finite Fourier Transform

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 >>

# Touch-Tone Telephone Dialing8

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 Differentiation3

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 >>

# CHEBFUN, Snake2

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

# CHEBFUN, Roots

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 >>

# CHEBFUN, Numerical Computing With Functions

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 >>