Richard Brent's improvements to Dekker's zeroin algorithm, published in 1971, made it faster, safer in floating point arithmetic, and guaranteed not to fail. ... read more >>

Th. J. Dekker's zeroin algorithm from 1969 is one of my favorite algorithms. An elegant technique combining bisection and the secant method for finding a zero of a function of a real variable, it has become fzero in MATLAB today. This is the first of a three part series.... read more >>

Augustin (Austin) Dubrulle deserves to be better known in the numerical linear algebra community. His version of the implicit QR algorithm for computing the eigenvalues of a symmetric tridiagonal matrix that was published in a half-page paper in Numerische Mathematik in 1970 is faster than Wilkinson's version published earlier. It is still a core algorithm in MATLAB today. ... read more >>

This is the third in a multi-part series on the MATLAB random number generators. MATLAB has used variants of George Marsaglia's ziggurat algorithm to generate normally distributed random numbers for almost twenty years. ... read more >>

This is the second of a multi-part series about the MATLAB random number generators. If you ask for help rng, you will get lots of information, including the fact that there are three modern generators.... read more >>

This is the first of a multi-part series about the MATLAB random number generators.... read more >>

Single and double precision are combined to facilitate a triple precision accumulated inner product.... read more >>

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 >>