Backward error analysis of cyclic reduction for the solution of tridiagonal systems

Abstract

Tridiagonal systems play a fundamental role in matrix computation. In particular, in recent years parallel algorithms for the solution of tridiagonal systems have been developed. Among these, the cyclic reduction algorithm is particularly interesting. Here the stability of the cyclic reduction method is studied under the assumption of diagonal dominance. A backward error analysis is made, yielding a representation of the error matrix for the factorization and for the solution of the linear system. The results are compared with those for LU factorization.