Analysis of a Fast Hankel Eigenvalue Algorithm
نویسنده
چکیده
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 results from numerical experiments.
منابع مشابه
Calculation of One-dimensional Forward Modelling of Helicopter-borne Electromagnetic Data and a Sensitivity Matrix Using Fast Hankel Transforms
The helicopter-borne electromagnetic (HEM) frequency-domain exploration method is an airborne electromagnetic (AEM) technique that is widely used for vast and rough areas for resistivity imaging. The vast amount of digitized data flowing from the HEM method requires an efficient and accurate inversion algorithm. Generally, the inverse modelling of HEM data in the first step requires a precise a...
متن کاملParallel Computation of the Eigenstructure of Toeplitz-plus-Hankel Matrices on Multicomputers
In this paper we present four parallel algorithms to compute any group of eigenvalues and eigenvectors of a Toeplitz-plus-Hankel matrix. These algorithms parallelize a method that combines the bisection technique with a fast root-finding procedure to obtain each eigenvalue. We design a parallel algorithm that applies a static distribution of the calculations among processors and three algorithm...
متن کاملFast Hankel tensor-vector product and its application to exponential data fitting
This paper is contributed to a fast algorithm for Hankel tensor–vector products. First, we explain the necessity of fast algorithms for Hankel and block Hankel tensor–vector products by sketching the algorithm for both one-dimensional and multi-dimensional exponential data fitting. For proposing the fast algorithm, we define and investigate a special class of Hankel tensors that can be diagonal...
متن کامل