Analysis of a parallel solution method for tridiagonal linear systems

We analyse an alternative decomposition for a tridiagonal matrix which has the property that the decomposition as well as the subsequent solution process can be done in two parallel parts. This decomposition is equivalent to the two-sided Gaussian elimination algorithm that has been discussed by Babuska. In the context of parallel computing a similar approach has been suggested by Joubert and Cloete. The computational complexity of this alternative decomposition is the same as for the standard decomposition and a remarkable aspect is that it often leads to slightly more accurate solutions than the standard process does. The algorithm can be combined with recursive doubling or cyclic reduction in order to increase the degree of parallelism and vectorizability.