A fast Solver for Pentadiagonal Toeplitz Systems

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.