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Shahin Hasanbeigi

Publications and source records attributed to Shahin Hasanbeigi.

3 recordsLinked to original sources
arXiv2024

A New Fast Direct Method For Solving Quasi-Toeplitz System of Equations

The objective of this study is to present a novel, efficient, and fast direct method for solving linear systems of equations whose coefficient matrix is a tridiagonal Quasi-Toeplitz matrix. Such matrices are frequently encountered in the discretization of second-order differential equation problems with Neumann boundary conditions, the discretization of Quasi-Birth-and-Death processes known as QBD matrix equations, and other related applications. The presented method has been demonstrated to produce favorable results in terms of run time for moderately large systems when compared to classical direct methods, such as the LU and PLU methods.

math.NA↗
arXiv2024

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.

math.NA↗