The Householder Transformation, Swiss Army Knife of Numerical Linear Algebra
In this talk I will define the Householder transformation, then immediately put
it to work in several ways:
* To illustrate the usefulness of geometry to elegantly derive and prove
seemingly algebraic properties of the transform;
* To demonstrate an underappreciated use of the Householder transform for
numerical linear algebra -- specifically, for matrix determinants and
inverses;
* To show how geometric notions of determinant and matrix norm can be used
to easily understand round-off error in Householder and Gaussian-elimination
methods;
* To prove that not only the applied grads can have fun with numerical
techniques; and
* To give an application of Householder transforms to dumb on-board processors,
subtitled "What I did over the winter break while the rest of you were having
a real vacation."
John Kerl
Graduate Student Colloquium
January 25, 2007