Analytically Explicit Inverse of a Kind of Periodic Tridiagonal Matrix Using a Backward Continued Fraction Approach

Abstract

We present a fast algorithm for generating the inverse and the determinant of an extended, periodic, tridiagonal matrix. We use backward continued fractions to generate the elements of the inverse in closed form. By trading memory use against the cost of repeating the computation of certain quantities we are able to produce an effective procedure for a symbolic algebra implementation. We compare the performance of our Maple implementation with that of the standard Maple library procedures for matrix inversion and computation of the determinant on a set of illustrative example matrices. © 2022, Wilmington Scientific Publisher. All rights reserved.