  The objective of this work is to present a novel approach for the solution of
Pentadiagonal Toeplitz systems of equations that is both faster and more
effective than existing classical direct methods. The distinctive structure of
Pentadiagonal Toeplitz matrices can be leveraged to devise an algorithm for
solving upper triangle systems, rather than the original system. This approach
is considerably more straightforward and expeditious than classical methods
such as LU and Gauss Eliminations. A comparison with the LU and PLU methods
demonstrates the efficacy of our novel algorithm. Furthermore, numerical tests
substantiate this efficacy.
