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. ... 続きを読む >>

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.... 続きを読む >>

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. ... 続きを読む >>

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. ... 続きを読む >>

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.... 続きを読む >>

This is the first of a multi-part series about the MATLAB random number generators.... 続きを読む >>

Single and double precision are combined to facilitate a triple precision accumulated inner product.... 続きを読む >>

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.... 続きを読む >>

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.... 続きを読む >>

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 . ... 続きを読む >>