Monthly Archives: March 2016

The Top 10 Algorithms in Applied Mathematics

In the January/February 2000 issue of Computing in Science and Engineering, Jack Dongarra and Francis Sullivan chose the “10 algorithms with the greatest influence on the development and practice of science and engineering in the 20th century” and presented a … Continue reading

Posted in Princeton Companion | 1 Comment

A Collection of Invalid Correlation Matrices

I’ve written before (here) about the increasingly common problem of matrices that are supposed to be correlation matrices (symmetric and positive semidefinite with ones on the diagonal) turning out to have some negative eigenvalues. This is usually bad news because … Continue reading

Posted in research | Tagged , | Leave a comment

Behind the Scenes of the Princeton Companion to Applied Mathematics

I’ve published an article Making the Princeton Companion to Applied Mathematics in Mathematics Today, the membership magazine of the The Institute of Mathematics and its Applications. The article describes the story behind the Princeton Companion to Applied Mathematics, published in … Continue reading

Posted in Princeton Companion | Tagged | Leave a comment

Empty Matrices in MATLAB

What matrix has zero norm, unit determinant, and is its own inverse? The conventional answer would be that there is no such matrix. But the empty matrix [ ] in MATLAB satisfies these conditions: >> A = []; norm(A), det(A), … Continue reading

Posted in matrix computations | Tagged | 1 Comment

Updated Catalogue of Software for Matrix Functions

Edvin Deadman and I have updated the catalogue of software for matrix functions that we produced in 2014 (and which was discussed in this post). The new version, which has undergone some minor reorganization, is available here. It covers what … Continue reading

Posted in software | Tagged , , , | Leave a comment

The Improved MATLAB Functions Expm and Logm

The matrix exponential is a ubiquitous matrix function, important both for theory and for practical computation. The matrix logarithm, an inverse to the exponential, is also increasingly used (see my earlier post, 400 Years of Logarithms). MATLAB R2015b introduced new … Continue reading

Posted in research | Tagged , | Leave a comment