Explicit and asymptotic formulas for \(LDM^ t\) factorization of banded Toeplitz matrices
Let \(T\) be a banded Toeplitz matrix. Then \(T= LDM^t\), where \(L\) and \(M\) are unipotent lower triangular banded matrices and \(D\) is a diagonal matrix. There are well-known recursion formulas for the entries of \(L\), \(M\), and \(D\). The author gives conditions under which the sequence formed by the entries in any subdiagonal of \(L\) or \(M\) is converging exponentially, i.e. for very large dimensions \(L\) and \(M\) are approximately Toeplitz, and the sequence formed by the diagonal \(D\) converges exponentially.
scientific article; zbMATH DE number 778238