A fast algorithm for solving special tridiagonal systems

In this paper, a fast algorithm for solving the special tridiagonal system is presented. This special tridiagonal system is a symmetric diagonally dominant and Toeplitz system of linear equations. The error analysis is also given. Our algorithm is quite competitive with the Gaussian elimination, cyclic reduction, specialLU factorization, reversed triangular factorization, and Toeplitz factorization methods. In addition, our result can be applied to solve the near-Toeplitz tridiagonal system. Some examples demonstrate the good efficiency and stability of our algorithm.ZusammenfassungIn dieser Arbeit wird ein schneller Algorithmus zur Lösung symmetrischer, diagonaldominanter tridiagonaler Töpflitz-Systeme vorgestellt. Auch eine Fehleranalyse liegt vor. Der Algorithmus ist den folgenden Verfahren mindestens gleichwertig: Gauss-Elimination, zyklische Reduktion, spezielleLU-Faktorisierung, umgekehrte Faktorisierung, Töplitz-Faktorisierung. Außerdem kann unser Vorgehen zur Lösung in tridiagonalen fast-Töplitz-Systemen verwendet werden. Einige Beispiele zeigen die Effizienz und Stabilität unseres Algorithmus.

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