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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

Block Factorization of Hankel Matrices and Euclidean Algorithm