On the solutions of tridiagonal linear systems

Tridiagonal linear systems are of special importance being appeared in space researches and also in several well-known algorithms. There are many methods for solving a tridiagonal linear system. Most of them are suffering from the accumulation of the round off errors. In this paper a new method will be given to overcome the defects of the other methods. Also, two direct methods, for solving a system of linear equations having matrices of quaternion entries as coefficients and independent terms, are proposed. Second kind Chebyshev polynomials, in a matrix argument, are used as a tool to do certain calculations.