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.