(Please replace the erroneous posting from yesterday, Nov. 28, with this corrected version.)... 続きを読む >>

Here is a very short course in Linear Algebra. The Singular Value Decomposition provides a natural basis for Gil Strang's Four Fundamental Subspaces.... 続きを読む >>

My favorite ordinary differential equation provides a good test of ODE solvers, both numeric and symbolic. It also provides a nice illustration of the underlying existence theory and error analysis.... 続きを読む >>

I am launching a project that I call Cleve's Laboratory. My most recent Cleve's Corner column in MathWorks News & Notes is about the project. The MATLAB app itself is available for download from the MATLAB Central File Exchange.... 続きを読む >>

This is a follow-up to my previous follow-up, posted several days ago. A very careful reader, Bruno Bazzano, contributed a comment pointing out what he called "a small typo" in my code for the classic Gram-Schmidt algorithm. It is more than a small typo, it is a serious blunder. I must correct the code, then do more careful experiments and reword my conclusions.... 続きを読む >>

This is a follow-up to my previous post. 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 >>

The QR decomposition is often the first step in algorithms for solving many different matrix problems, including linear systems, eigenvalues, and singular values. Householder reflections are the preferred tool for computing the QR decomposition.... 続きを読む >>

A new app employs transformations of a graphic depicting a house to demonstrate matrix multiplication.... 続きを読む >>

MATLAB Central is celebrating its 15th birthday this fall. In honor of the occasion, MathWorks bloggers are reminiscing about their first involvement with the Web site. My first contribution to the File Exchange was not MATLAB software, but rather a collection of documents that I called the Pentium Papers. I saved this material in November and December of 1994 when I was deeply involved in the Intel Pentium Floating Point Division Affair…. 続きを読む >>

Jim Sanderson has had a fascinating professional life. He was my PhD student in math at the University of New Mexico in the 1970s. He spent almost 20 years as a computational scientist at Los Alamos National Laboratory, working on the lab’s supercomputers. He then developed an interest in ecology, went back to school, and is now the world’s leading authority on the preservation of small wild cats around the world…. 続きを読む >>