Posts 31 - 40 of 45

Results for: Algorithms

Dubrulle Creates A Faster Tridiagonal QR Algorithm

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 >>

The Ziggurat Random Normal Generator

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 >>

Parallel Random Number Generators

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 >>

Random Number Generators, Mersenne Twister

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

Triple Precision Accumlated Inner Product 1

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

Iterative Refinement for Solutions to Linear Systems 4

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 Dialing 8

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 3

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 1

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 >>

Posts 31 - 40 of 45