URI Chapter Sponsor Applied Mathematics Seminar Monday 10:00-10:50 AM Lippitt Hall, Room 201

 Fall 2009 September 21 James Baglama Title: Numerical Approximation of the Product of the Square Root October 12 Tom Bella TitleUsing Unitary Hessenberg Matrices to Factor Projectors A recent paper by Barszcz and Parlett began with the paragraph: "Ask a student to specify an n x n orthogonal matrix with a given first column q and a well trained one will name the Householder reflector [snip]. Ask for a different solution and, perhaps, you will be told to use n-1 Givens rotations [snip] with carefully chosen rotation angles. Ask for yet another solution and, in all probability, you will be met with silence." The paper then proceeds to give a third option, using a factorization of a projector matrix. This talk will give details of these three solutions, the third of which we'll explain in the context of unitary Hessenberg matrices. Time permitting, our work in generalizing these results will be discussed. This talk will be at a very accessible level and will assume very little. We'll begin with explanations of Householder reflections and Given's rotations, and their central role in Numerical Linear Algebra. November 2 ----- Canceled. November 23 Tom Bella Title: Using Unitary Hessenberg Matrices to Factor Projectors A recent paper by Barszcz and Parlett began with the paragraph: "Ask a student to specify an n x n orthogonal matrix with a given first column q and a well trained one will name the Householder reflector [snip]. Ask for a different solution and, perhaps, you will be told to use n-1 Givens rotations [snip] with carefully chosen rotation angles. Ask for yet another solution and, in all probability, you will be met with silence." The paper then proceeds to give a third option, using a factorization of a projector matrix. This talk will give details of these three solutions, the third of which we'll explain in the context of unitary Hessenberg matrices. Time permitting, our work in generalizing these results will be discussed. This talk will be at a very accessible level and will assume very little. We'll begin with explanations of Householder reflections and Given's rotations, and their central role in Numerical Linear Algebra.

Organized by: James Baglama, Tom Bella, and Li Wu