# Block Factorization of Hankel Matrices and Euclidean Algorithm

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 7, page 48-54
- ISSN: 0973-5348

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topBelhaj, S.. Taik, A., ed. "Block Factorization of Hankel Matrices and Euclidean Algorithm." Mathematical Modelling of Natural Phenomena 5.7 (2010): 48-54. <http://eudml.org/doc/197675>.

@article{Belhaj2010,

abstract = {It is shown that a real Hankel matrix admits an approximate block diagonalization in
which the successive transformation matrices are upper triangular Toeplitz matrices. The
structure of this factorization was first fully discussed in [1]. This approach is
extended to obtain the quotients and the remainders appearing in the Euclidean algorithm
applied to two polynomials u(x) and
v(x) of degree n and
m, respectively, whith m <
n},

author = {Belhaj, S.},

editor = {Taik, A.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {block factorization; Hankel matrices; Toeplitz matrices; Euclidean algorithm},

language = {eng},

month = {8},

number = {7},

pages = {48-54},

publisher = {EDP Sciences},

title = {Block Factorization of Hankel Matrices and Euclidean Algorithm},

url = {http://eudml.org/doc/197675},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Belhaj, S.

AU - Taik, A.

TI - Block Factorization of Hankel Matrices and Euclidean Algorithm

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/8//

PB - EDP Sciences

VL - 5

IS - 7

SP - 48

EP - 54

AB - It is shown that a real Hankel matrix admits an approximate block diagonalization in
which the successive transformation matrices are upper triangular Toeplitz matrices. The
structure of this factorization was first fully discussed in [1]. This approach is
extended to obtain the quotients and the remainders appearing in the Euclidean algorithm
applied to two polynomials u(x) and
v(x) of degree n and
m, respectively, whith m <
n

LA - eng

KW - block factorization; Hankel matrices; Toeplitz matrices; Euclidean algorithm

UR - http://eudml.org/doc/197675

ER -

## References

top- S. Belhaj. A fast method to block-diagonalize a Hankel matrix. Numer Algor, 47 (2008), 15-34.
- S. Belhaj. Block diagonalization of Hankel and Bézout matrices : connection with the Euclidean algorithm, submitted.
- N. Ben Atti, G.M. Diaz-Toca. Block diagonalization and LU-equivalence of Hankel matrices. Linear Algebra and its Applications, 412 (2006), 247-269.
- D. Bini, L. Gemignani. On the Euclidean scheme for polynomials having interlaced real zeros. Proc. 2nd ann. ACM symp. on parallel algorithms and architectures, Crete, (1990), 254-258.
- D. Bini, L. Gemignani. Fast parallel computation of the polynomial remainder sequence via Bézout and Hankel matrices. SIAM J. Comput., 24 (1995), 63–77.
- A. Borodin, J. VonZurGathen, J. Hopcroft. Fast parallel matrix and gcd computation. Information and Control, 52 (1982), 241-256.
- G. Diaz-Toca, N. Ben Atti. Block LU factorization of Hankel and Bezout matrices and Euclidean algorithm. Int. J. Comput. Math., 86 (2009), 135-149.
- W. B. Gragg, A. Lindquist. On partial realization problem. Linear Algebra Appl., 50 (1983), 277-319.
- G. Heining, K. Rost. Algebraic methods for Toeplitz-like matrices and operators. Birkhäuser Verlag, Basel, 1984.

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