A fast eigenvalue algorithm for Hankel matrices

Analysis of a Fast Hankel Eigenvalue Algorithm

This paper analyzes the important steps of an O(n 2 log n) algorithm for nding the eigenvalues of a complex Hankel matrix. The three key steps are a Lanczos-type tridiagonalization algorithm, a fast FFT-based Hankel matrix-vector product procedure, and a QR eigenvalue method based on complex-orthogonal transformations. In this paper, we present an error analysis of the three steps, as well as r...

Analysis of a Fast Eigenvalue Algorithm for Hankel Matri es

A Fast Eigenvalue Algorithm for Hankel Matri es

A fast symmetric SVD algorithm for square Hankel matrices

This paper presents an O(n2 log n) algorithm for computing the symmetric singular value decomposition of square Hankel matrices of order n, in contrast with existing O(n3) SVD algorithms. The algorithm consists of two stages: first, a complex square Hankel matrix is reduced to a complex symmetric tridiagonal matrix using the block Lanczos method in O(n2 log n) flops; second, the singular values...

A fast implicit QR eigenvalue algorithm for companion matrices

Article history: Received 5 November 2008 Accepted 3 August 2009 Available online 4 September 2009 Submitted by V. Olshevsky AMS classification: 65F15 65H17