G. Heinig, K. Rost: Fast Algorithms for Toeplitz and Hankel Matrices

Author(s):

G. Heinig

K. Rost

Title:

G. Heinig, K. Rost: Fast Algorithms for Toeplitz and Hankel Matrices

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 21, 2010

Mathematics Subject Classification:

65F05	[]
15B05	[]
15A06	[]
15A23	[]

Abstract:

The paper gives a self-contained survey of fast algorithms for solving linear systems of equations with Toeplitz or Hankel coefficient matrices. It is written in the style of a textbook. Algorithms of Levinson-type and of Schur-type are discussed. Their connections with triangular factorizations, Padè recursions and Lanczos methods are demonstrated. In the case in which the matrices possess additional symmetry properties, split algorithms are designed and their relations to butterfly factorizations are developed.

Keywords:

Toeplitz matrix, Hankel matrix, Levinson algorithm, Schur algorithm, LU-factorization, ZW-factorization

Language:

English

Publication time:

11/2010