A fast algorithm for solving diagonally dominant symmetric pentadiagonal Toeplitz systems

Banded Toeplitz systems of linear equations arise in many application areas and have been well studied in the past. Recently, significant advancement has been made in algorithm development of fast parallel scalable methods to solve tridiagonal Toeplitz problems. In this paper we will derive a new algorithm for solving symmetric pentadiagonal Toeplitz systems of linear equations based upon a technique used in [J.M. McNally, L.E. Garey, R.E. Shaw, A split-correct parallel algorithm for solving tri-diagonal symmetric Toeplitz systems, Int. J. Comput. Math. 75 (2000) 303–313] for tridiagonal Toeplitz systems. A common example which arises in natural quintic spline problems will be used to demonstrate the algorithm’s effectiveness. Finally computational results and comparisons will be presented.