Explicit and asymptotic formulas for LDM^t factorization of banded toeplitz matrices

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. © 1995, All rights reserved.