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

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