I have an upper triangular Toeplitz matrix whose elements are block Toeplitz matrices as well. I need to factor this matrix as a poduct of two upper triangular block Toeplitz matrices having the same structure as the original matrix. Furthermore, the original matrix is rank defficient. An SVD will destroy the Toeplitz structure that I need. Does anyone know an algorithm that can do this? Any help will be appreciated.
what i know about this type of matrix is simply can be done by Matlab:
L=3;
N=5;
AA=[1;1.2;2;3.3;4.5];
a=toeplitz(AA(1:N),AA(1)*eye(1, L))
if you explain more, i mean by simple example may i can understand you point more.
my pleasure and most welcome.
The problem is like this. You have an upper block triangular Toeplitz matrix, say C, and you want to factor it as C = A*B, where A and B are two upper block triangular Toeplitz matrices. Meanwhile C ~ m x n is rank deficient, i.e, rank(C) = r < min{m,n}. Therefore, rank(A) = r and rank(B) = r.
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