Posts 31 - 40 of 45

結果: 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. ... 続きを読む >>

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. ... 続きを読む >>

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.... 続きを読む >>

Random Number Generators, Mersenne Twister

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

Triple Precision Accumlated Inner Product 1

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

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.... 続きを読む >>

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.... 続きを読む >>

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 . ... 続きを読む >>

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.... 続きを読む >>

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.... 続きを読む >>

Posts 31 - 40 of 45