Stable solution of tridiagonal systems (Q1281795)

Three pivoting strategies for solving general tridiagonal systems of linear equations are presented. The first strategy resembles the classical method of Gaussian elimination with no pivoting and is stable provided a simple and easily checkable condition is fulfilled. In the second strategy, the growth of the elements is monitored to ensure backward stability in the most cases. The third strategy makes also use of the right-hand side vector to make pivoting decisions and is proved to be backward stable. Numerical examples are presented which show the possibility of checking the stability of solutions for tridiagonal systems making use of the three pivoting strategies considered in the paper.