Posts 21 - 27 of 27

結果: Precision

The Pentium Papers — My First MATLAB Central Contribution

MATLAB Central is celebrating its 15th birthday this fall. In honor of the occasion, MathWorks bloggers are reminiscing about their first involvement with the Web site. My first contribution to the File Exchange was not MATLAB software, but rather a collection of documents that I called the Pentium Papers. I saved this material in November and December of 1994 when I was deeply involved in the Intel Pentium Floating Point Division Affair…. 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 >>

Floating Point Denormals, Insignificant But Controversial

Denormal floating point numbers and gradual underflow are an underappreciated feature of the IEEE floating point standard. Double precision denormals are so tiny that they are rarely numerically significant, but single precision denormals can be in the range where they affect some otherwise unremarkable computations. Historically, gradual underflow proved to be very controversial during the committee deliberations that developed the standard. ... 続きを読む >>

Floating Point Numbers 5

This is the first part of a two-part series about the single- and double precision floating point numbers that MATLAB uses for almost all of its arithmetic operations. (This post is adapted from section 1.7 of my book Numerical Computing with MATLAB, published by MathWorks and SIAM.) ... 続きを読む >>

Wilkinson’s Polynomials

Wilkinson's polynomials are a family of polynmials with deceptively sensitive roots.... 続きを読む >>

Reduced Penultimate Remainder 4

I investigated the reduced penultimate remainder algorithm in an undergraduate research project under professor John Todd at Caltech in 1961. I remember it today for two reasons. First, I learned what penultimate means. And second, it is the most obscure, impractical algorithm that I know. I suspect none of my readers have ever heard of it.... 続きを読む >>

Posts 21 - 27 of 27