We give explicit inverses of tridiagonal 2-Toeplitz and 3-Toeplitz matrices which generalize some well-known results concerning the inverse of a tridiagonal Toeplitz matrix.
Summary. We obtain explicit formulas for the entries of the inverse of a nonsingular and irreducible tridiagonal k−Toeplitz matrix A. The proof is based on results from the theory of orthogonal polynomials and it is shown that the entries of the inverse of such a matrix are given in terms of Chebyshev polynomials of the second kind. We also compute the characteristic polynomial of A which enables us to state some conditions for the existence of A −1 . Our results also extend known results for the case when the residue mod k of the order of A is equal to 0 or k − 1 (Numer. Math., 10 (1967), pp. 153-161.). Classification (2000): 15A09, 42C05, 33C45, 65Q05
Mathematics Subject
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