Fast numerical algorithms for solving opposite-bordered tridiagonal Toeplitz linear systems and their applications
Hcini Fahd · Results in Applied Mathematics · 2025
This paper presents two fast numerical algorithms for solving opposite-bordered tridiagonal Toeplitz linear systems . Both algorithms are designed to solve a system of n equations in linear time. The first algorithm uses a block 2 × 2 -LU factorization combined with a fast approach for solving upper quasi-triangular Toeplitz systems. The second algorithm applies a splitting technique to the opposite-bordered tridiagonal Toeplitz matrix , along with a fast algorithm for solving tridiagonal Toeplitz systems. The effectiveness of the proposed algorithms is demonstrated through numerical experiments.