Posts 11 - 20 of 94

Results for: Numerical Analysis

What is A\A?

The answer: A\A is always I, except when it isn't.... read more >>

Round, With Tie Breakers, A Prototype

In February and March I published three blog posts about an enhancement request for MATLAB concerning tie breakers with the round function, including the ability to round ties to even. Round One, Round Two and Round Three. Since then, a group of us at MathWorks, organized by my colleague (and academic great-great-grand-descendant) Heiko Weichelt, have been considering the request. We had a virtual design review recently. This post describes a prototype incorporating the features that were discussed at that review.... read more >>

Complexity of Computing the Eigenvalues of a Symmetric Matrix 1

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 Matrices 1

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

Solving Commodious Linear Systems 2

This is about linear systems with fewer equations than variables; A*x = b where the m -by- n matrix A has fewer rows that columns, so m < n . I have always called such systems wide or fat, but this is not respectful. So I consulted the Merriam-Webster Thesaurus and found commodious.... read more >>

Round, With Tie Breakers, Round Three 1

I recently published Round, With Ties to Even and followed that with Round Two. Then, in an email, Andy Bartlett pointed out that my new round function fails for some large values of x between flintmax/2 and flintmax.... read more >>

Round, With Tie Breakers, Round Two

I published Round, With Ties to Even a couple of days ago. Steve Eddins and Daniel Dolan immediately had substantive comments. Here is my reaction to their comments.... read more >>

Round, With Ties to Even 2

We are considering a MATLAB Enhancement Request to support options for round(x) when x is exactly halfway between two integers.... read more >>

CR and CAB, Rank Revealing Matrix Factorizations 5

The rank of a linear transformation is a fundamental concept in linear algebra and matrix factorizations are fundamental concepts in numerical linear algebra. Gil Strang's 2020 Vision of Linear Algebra seeks to introduce these notions early in an introductory linear algebra course.... read more >>

A Famous Equation, x^2 = 2^x

A recent episode of the popular YouTube channel "blackpenredpen" is about solutions to the famous equation... read more >>

Posts 11 - 20 of 94