This program is written by Egor Maximenko and Gabino Sánchez Arzate.
The formulas used in this program are based on the article by William F. Trench (1985): Explicit inversion formulas for Toeplitz band matrices. DOI: 10.1137/0606054
On this page we construct and visualize the inverse matrix T−1,
where T is the tridiagonal real symmetric Toeplitz matrix of order n,
with generating symbol g(x) = 4 (sin(x/2))2 + α.
We suppose that α > 0. In this case the matrix T is positive definite.
The first column of T is 2 + α, −1, 0, …, 0.
Choose the value of the parameter α and the order n of the matrix:
α = 0.5
n = 8
All these matrices are symmetric and persymmetric. Next picture shows the first column of S:
Code in MATLAB language (tested in GNU Octave)