A generalized unitary Hessenberg matrix

作者：Stewart Michael^*

来源：Linear Algebra and Its Applications, 2013, 439(12): 3807-3821.

DOI：10.1016/j.laa.2013.10.008

• Unitary Hessenberg matrix
• Isometric Arnoldi algorithm
• Toeplitz 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 Q R factorization of a Toeplitz-like matrix.

• 出版日期2013-12-15