Classical Gram-Schmidt and Modified Gram-Schmidt are two algorithms for orthogonalizing a set of vectors. Householder elementary reflectors can be used for the same task. The three algorithms have very different roundoff error properties…. 続きを読む >>

During the SIAM Annual Meeting this summer in Boston there will be a special minisymposium Wednesday afternoon, July 13, honoring Charlie Van Loan, who is retiring at Cornell. (I use "at" because he's not leaving Ithaca.) I will give a talk titled "19 Dubious Way to Compute the Zeros of a Polynomial", following in the footsteps of the paper about the matrix exponential that Charlie and I wrote in 1978 and updated 25 years later. I really don't have 19 ways to compute polynomial zeros, but then I only have a half hour for my talk. Most of the methods have been described previously in this blog. Today's post is mostly about "roots".... 続きを読む >>

Gil Strang has produced a MOOC-style video course on Differential Equations and Linear Algebra. I have added some videos about the MATLAB ODE suite. The series is available from the MathWorks Web site, MIT OpenCourseWare and several other popular sources.... 続きを読む >>

When a deck of playing cards is shuffled perfectly, the result is not random. A perfect shuffle places the cards in a mathematically precise order. As a result, when the most common version of a perfect shuffle is repeated eight times, the deck returns to its original state.... 続きを読む >>

I got the idea for these test matrices from Gene Golub years ago, but the mathematical foundation comes from a paper by Divakar Viswanath and Nick Trefethen. ... 続きを読む >>

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.... 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 >>

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.... 続きを読む >>

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.... 続きを読む >>

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