A look at the structure, and the eigenvalues and singular values of interesting test matrices.... read more >>

I introduced Sonic in my blog post last month. Today I will use Sonic to add sound to the graphics from three old posts, the vibrating L-shaped membrane, the Recamán sequence and the chaotic behavior of the Swinging Sticks.... read more >>

This is post number 300 of Cleve's Corner blog. The first post was on June 6, 2012, which is 600 weeks ago. So, I have averaged one post every two weeks for over a decade. The posts were more frequent in the early days and are less frequent today.... read more >>

(The January 5 posting was premature and incomplete.)... read more >>

I am giving a five-minute talk today, May 26, at the virtual seminar on Complexity of Matrix Computations. Here are my slides. Two new MATLAB functions, tred and imtql, instrumented to count flops, are available in symeig.m.... read more >>

Computing Eigenvalues of Symmetric MatricesSee revision.Get the MATLAB code (requires JavaScript) Published with MATLAB®... read more >>

Recently, I had email from a student in Italy.... read more >>

While I was working on my posts about Pejorative Manifolds, I was pleased to discover the intriguing patterns created by the roundoff error in the computed eigenvalues of triple Kronecker products.... read more >>

In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold. In case you don't use it in everyday conversation, pejorative means "expressing contempt or disapproval."... read more >>

The QR algorithm is one of the world's most successful algorithms. We can use animated gifs to illustrate three variants of the algorithm, one for computing the eigenvalues of a nonsymmetric... read more >>