Block Factorization of Hankel Matrices and Euclidean Algorithm
نویسنده
چکیده
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.
منابع مشابه
Inversion Components of Block Hankel-like Matrices
The inversion problem for square matrices having the structure of a block Hankel-like matrix is studied. Examples of such matrices in&de Hankel striped, Hankel layered, and vector Hankel matrices. It is shown that the components that both determine nonsingularity and construct the inverse of such matrices are closely related to certain matrix polynomials. These matrix polynomials are multidimen...
متن کاملKronecker product approximations for dense block Toeplitz-plus-Hankel matrices
In this paper, we consider the approximation of dense block Toeplitz-plus-Hankel matrices by sums of Kronecker products. We present an algorithm for efficiently computing the matrix approximation that requires the factorization of matrices of much smaller dimension than that of the original. The main results are described for block Toeplitz matrices with Toeplitz-plus-Hankel blocks (BTTHB), but...
متن کاملTransformation Techniques for Toeplitz and Toeplitz-plus-hankel Matrices Part Ii. Algorithms
In the rst part 13] of the paper transformationsmappingToeplitz and Toeplitz-plus-Hankel matrices into generalizedCauchy matrices were studied. In this second part fast algorithms for LU-factorization and inversion of generalized Cauchy matrices are discussed. It is shown that the combinationof transformation pivoting techniques leads to algorithms for indeenite Toeplitz and Toeplitz-plus-Hanke...
متن کاملFast Algorithms for Structured Least Squares and Total Least Squares Problems
We consider the problem of solving least squares problems involving a matrix M of small displacement rank with respect to two matrices Z 1 and Z 2. We develop formulas for the generators of the matrix M (H) M in terms of the generators of M and show that the Cholesky factorization of the matrix M (H) M can be computed quickly if Z 1 is close to unitary and Z 2 is triangular and nilpotent. These...
متن کاملQR-factorization of displacement structured matrices using a rank structured matrix approach
A general scheme is proposed for computing the QR-factorization of certain displacement structured matrices, including Cauchy-like, Vandermonde-like, Toeplitz-like and Hankel-like matrices, hereby extending some earlier work for the QR-factorization of the Cauchy matrix. The algorithm employs a chasing scheme for the recursive construction of a diagonal plus semiseparable matrix of semiseparabi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011