Stable solution to tridiagonal systems

In this paper we present three different pivoting strategies for solving general tridiagonal systems of linear equations. The first strategy resembles the classical method of Gaussian elimination with no pivoting and is stable provided a simple and easily checkable condition is met. In the second strategy, the growth of the elements is monitored so as to ensure backward stability in most cases. Finally, the third strategy also uses the right-hand side vector to make pivoting decisions and is proved to be unconditionally backward stable.