EXPLICIT AND ASYMPTOTIC FORMULAS FOR LDM(T) FACTORIZATION OF BANDED TOEPLITZ MATRICES

摘要

We study the LDM(t) 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. [References: 19]