My colleagues are looking for a matrix to be used in a new benchmark. They've come to the right place.... 続きを読む >>

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... 続きを読む >>

I have just returned from the ICIAM2019 conference in Valencia, Spain. It was a huge conference -- 4,000+ attendees, dozens of prize and invited talks, hundreds of parallel minisympsia. I gave a talk in a two-part minisymposium organized by Nick Higham and Rob Corless. I outlined the first part of the talk in this blog a month ago. This post outlines the second part, which was about Hadamard matrices. Some of it is taken from a post in this blog five years ago.... 続きを読む >>

(This is a reprint of the second ever Cleve's Corner from the Winter 1990 MathWorks Newsletter).The other day at lunch with a couple of other MathWorks people, I posed the following... 続きを読む >>

We will have a two-part minisymposium on "Bohemian Matrices" at ICIAM2019, the International Congress on Industrial and Applied Mathematics in Valencia, Spain, July 15-19. This is an outline of my talk.... 続きを読む >>

This is a summary of my talk at the conference Celebrating the Centenary of James H. Wilkinson's Birth at the University of Manchester, May 29.... 続きを読む >>

On May 29-30, I plan to attend a conference, organized by Nick Higham, at the University of Manchester. The title of the conference is... 続きを読む >>

I recently acquired a GPU, a graphics processing unit. It's called a GPU because such processors were originally intended to speed up graphics. But MATLAB uses it to speed up computation. Let's see how the gpuArray object benchmarks on my machine. I have been doing computer benchmarks for years. I like to do profiles where I vary the size of a task and see how the amount of memory required affects performance. I always learn something unexpected when I do these profiles. Ben Todoroff is on the MathWorks Parallel Processing team. Last year he contributed #34080, gpuBench to the MATLAB Central File Exchange. He has been able to compare several different GPUs. I am going to consider the performance of only one GPU, but in more detail. Important note. This is only about double precision. Single precision is another story. ... 続きを読む >>

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.... 続きを読む >>

I probably first saw this matrix in 1960 in John Todd's class at Caltech. But I forgot about it until Tahar Loulou jogged my memory with a comment following my blog post in late May. It deserves a place in our gallery of interesting matrices.... 続きを読む >>