The inverse of a tridiagonal matrix

In this paper, explicit formulae fur the elements of the inverse of a general tridiagonal matrix are presented by first extending results on the explicit solution of a second-order linear homogeneous difference equation with variable coefficients to the nonhomogeneous case. and then applying these extended results to ii boundary value problem. A formula for the characteristic polynomial is obtained in the process. We also establish a connection between the matrix inverse and orthogonal polynomials. In addition, the case of a cyclic tridiagonal system is discussed. (C) 2001 Elsevier Science Inc. All rights reserved. AMS classification: 15A09; 39A10.