Purdue University Numerical Linear Algebra Group

January 15, 2015 at Purdue University.

Talk given:

Krylov and QR and polynomials

We will discuss

• the QR decomposition of a Krylov matrix for A and b, in terms of the Arnoldi/Hessenberg factorization of A.
• the Companion matrix as a special case of Hessenberg matrices
• the Vandermonde matrix as a special case of a Krylov matrix.
• root-finding and interpolation of polynomials via the Companion matrix