Posts 71 - 80 of 101

Results for: Matrices

Tumbling Box ODE 2

A rectangular box, such as a book or a cell phone, thrown in the air can tumble stably about its longest axis, or about its shortest axis, but not about its middle axis.... read more >>

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 >>

ALGOL 60, PL/0 and MATLAB 1

The 1960 programming language ALGOL 60 influenced the design of many subsequent languages, including C and a miniature language called PL/0. I based the design of the first MATLAB on PL/0.... read more >>

Friedrich Bauer 5

Fritz Bauer, eminent German computer scientist and last surviving member of the organizing committee of the 1964 Gatlingburg Conference on Numerical Algebra, passed away on March 26 at the age of 90.... 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 >>

Finite Fourier Transform Matrix

This is the third in a series of posts on the finite Fourier transform. The Fourier matrix produces an interesting graphic and has a surprising eigenvalue distribution. ... read more >>

Complete Pivoting and Hadamard Matrices 1

For several years we thought Hadamard matrices showed maximum element growth for Gaussian elimination with complete pivoting. We were wrong. ... read more >>

Gaussian Elimination with Partial Pivoting 1

In rare cases, Gaussian elimination with partial pivoting is unstable. But the situations are so unlikely that we continue to use the algorithm as the foundation for our matrix computations.... read more >>

Singular Value Analysis of Cryptograms

The Singular Value Decomposition of the digram frequency matrix of a text coded with a simple substitution cypher can reveal information about the vowels and consonants in the text. ... read more >>

Posts 71 - 80 of 101