Explicit and asymptotic formulas for LDMt factorization of banded toeplitz matrices Original Research Article

We study the LDMt factorization of banded Toeplitz matrices. We show that, under fairly general conditions, the L, M, and D factors exhibit exponential convergence along diagonals. We also give explicit formulas for the limiting values. Our method of proof involves a generalization to matrices of the theory of continued fractions of quadratic irrationals.