Vectorized algorithms for solving special tridiagonal systems (Q679289)

Two fast vectorized algorithms for solving a special tridiagonal system of the form \(A_nx=b\) are presented. Both new algorithms consist of three phases and only differ in the second phase. The first phase is a Toeplitz factorization of a slightly perturbed matrix of \(A_n\). The second phase is to solve the perturbed problem in a highly vectorized way, but only scale \(\times\) vector operations are involved. In the third phase, the solution to the original problem is recovered from the solution to the perturbed problem. Some error analyses are also given. In addition, some experimental results are illustrated on CRAY X-MP EA/116Se.