Results for: Eigenvalues

The QR Algorithm Computes Eigenvalues and Singular Values

Posted by Cleve Moler,

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 matrix, one for a symmetric matrix, and one for the singular values of a rectangular matrix. In all three cases, the QR iteration itself is preceded by a reduction to a compact form. All transformations are orthogonal similarities using Givens and Householder transformations. These are numerically stable, preserve eigenvalues, and preserve any symmetry.... read more >>

Experiments with Variable Format Half Precision

Posted by Cleve Moler,

For the past month I have been working with the variable format 16-bit floating point arithmetic that I described in this post. It has been frustrating work. I have found that the limited precision and limited range of half precision make it barely usable for the kind of experiments with matrix computation that I like to do. In this post I will describe a few of these experiments.... read more >>

EISPACK, Matrix Eigensystem Routines

Posted by Cleve Moler,

The ACM Special Interest Group on Programming Languages, SIGPLAN, expects to hold the fourth in a series of conferences on the History of Programming Languages in 2020, see HOPL-IV. The first drafts of papers are to be submitted by August, 2018. That long lead time gives me the opportunity to write a detailed history of MATLAB. I plan to write the paper in sections, which I'll post in this blog as they are available. This is the second such installment.... read more >>

Bug Report Revives Interest in SVD Option of “Eigshow”

Posted by Cleve Moler,

A few days ago we received email from Mike Hennessey, a mechanical engineering professor at the University of St. Thomas in St. Paul, Minnesota. He has been reading my book “Numerical Computing with MATLAB” very carefully. Chapter 7 is about “Eigenvalues and Singular Values” and section 10.3 is about one of my all-time favorite MATLAB demos, eigshow. Mike discovered an error in my description of the svd option of eigshow that has gone unnoticed in the over ten years that the book has been available from both the MathWorks web site and SIAM…. read more >>