منابع مشابه
LU -factorization of Block Toeplitz Matrices
We give a review of the theory of factorization of block Toeplitz matrices of the type T = (Ti−j)i,j∈Zd , where Ti−j are complex k × k matrices, in the form T = LDU, with L and L−1 lower block triangular, U and U−1 upper block triangular Toeplitz matrices, and D a diagonal matrix function. In particular, it is discussed how decay properties of Ti a ect decay properties of L, L−1, U , and U−1. W...
متن کاملSparse block factorization of saddle point matrices
The factorization method presented in this paper takes advantage of the special structures and properties of saddle point matrices. A variant of Gaussian elimination equivalent to the Cholesky’s factorization is suggested and implemented for factorizing the saddle point matrices block-wise with small blocks of order 1 and 2. The Gaussian elimination applied to these small blocks on block level ...
متن کاملBlock Factorization of Hankel Matrices and Euclidean Algorithm
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 ...
متن کاملSpectral Factorization of 2-block Toeplitz Matrices and Refinement Equations
Pairs of 2-block Toeplitz (N×N)-matrices (Ts)ij = p2i−j+s−1, s = 0, 1, i, j ∈ {1, . . . , N}, are considered for arbitrary sequences of complex coefficients p0, . . . , pN . A complete spectral resolution of the matrices T0, T1 in the system of their common invariant subspaces is obtained. A criterion of nondegeneracy and of irreducibility of these matrices is derived, and their kernels, root s...
متن کاملSpectral factorization of bi-infinite multi-index block Toeplitz matrices
In this paper we formulate a theory of LU and Cholesky factorization of bi-infinite block Toeplitz matrices A = (Ai−j )i,j∈Zd indexed by i, j ∈ Zd and develop two numerical methods to compute such factorizations. © 2002 Elsevier Science Inc. All rights reserved.
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ژورنال
عنوان ژورنال: Science in China Series F
سال: 2004
ISSN: 1009-2757
DOI: 10.1360/02yf0499