Washington State University
Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar
Department of Mathematics
Neill Hall 5W
September 28, Monday, 4:10 - 5:00 PM
Thomas R. Cameron
Department of Mathematics
Washington State University
Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar
Department of Mathematics
Neill Hall 5W
September 28, Monday, 4:10 - 5:00 PM
Thomas R. Cameron
Department of Mathematics
Washington State University
Title: Constructive Proof of Hessenberg Form
Abstract: Every real and complex matrix is unitarily similar to matrix in Hessenberg form. This similarity transformation can be done in a finite number of steps. Moreover, the QR and QZ algorithms are made cost efficient by a preliminary reduction to Hessenberg and Hessenberg-Triangular form, respectively.
A matrix polynomial, P(z), is a matrix whose entries are scalar polynomials with real or complex coefficients. In this talk we will present a construction of Hessenberg form for matrix polynomials. A preliminary reduction to Hessenberg form has the possibility of making several algorithms for computing the eigenvalues of a matrix polynomial cost efficient.
We will conclude with possible areas of future research, which include numerically stable algorithms for computing this Hessenberg form.
Abstract: Every real and complex matrix is unitarily similar to matrix in Hessenberg form. This similarity transformation can be done in a finite number of steps. Moreover, the QR and QZ algorithms are made cost efficient by a preliminary reduction to Hessenberg and Hessenberg-Triangular form, respectively.
A matrix polynomial, P(z), is a matrix whose entries are scalar polynomials with real or complex coefficients. In this talk we will present a construction of Hessenberg form for matrix polynomials. A preliminary reduction to Hessenberg form has the possibility of making several algorithms for computing the eigenvalues of a matrix polynomial cost efficient.
We will conclude with possible areas of future research, which include numerically stable algorithms for computing this Hessenberg form.