A generalized unitary Hessenberg matrix

This paper describes the use of a generalized isometric Arnoldi algorithm to reduce a unitary matrix, via unitary similarity, to a product of elementary reflectors and permutations. The computation is analogous to the reduction of a unitary matrix to a unitary Hessenberg matrix using the isometric Arnoldi algorithm. In the case in which A is a shift matrix, the reduction provides a novel recurrence for the factor R in the QR factorization of a Toeplitz-like matrix.