Computing the block factorization of complex Hankel matrices

In this paper, we present an algorithm for finding an approximate block diagonalization of complex Hankel matrices. Our method is based on inversion techniques of an upper triangular Toeplitz matrix, specifically, by simple forward substitution. We also consider an approximate block diagonalization...

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Bibliographic Details
Published in:Computing 2010-05, Vol.87 (3-4), p.169-186
Main Author: Belhaj, Skander
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Artificial Intelligence
Computer Appl. in Administrative Data Processing
Computer Communication Networks
Computer Science
Computer science
control theory
systems
Exact sciences and technology
Functional analysis
Information Systems Applications (incl.Internet)
Mathematical analysis
Mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Original Article
Sciences and techniques of general use
Software Engineering
Studies
Theoretical computing
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Summary:In this paper, we present an algorithm for finding an approximate block diagonalization of complex Hankel matrices. Our method is based on inversion techniques of an upper triangular Toeplitz matrix, specifically, by simple forward substitution. We also consider an approximate block diagonalization of complex Hankel matrices via Schur complementation. An application of our algorithm by calculating the approximate polynomial quotient and remainder appearing in the Euclidean algorithm is also given. We have implemented our algorithms in Matlab. Numerical examples are included. They show the effectiveness of our strategy.
ISSN:0010-485X
1436-5057
DOI:10.1007/s00607-010-0080-5