A note on the solution of narrow-banded Toeplitz systems

Abstract. This note observes that the \(LU\)-decomposition of narrow-banded Toeplitz matrices can be modified so that \(L\) and \(U\) are lower and upper band Toeplitz matrices plus a low rank correction matrix is added. The resulting method cannot be considered generally applicable however, it may be useful in special cases. For solving a system, the operation count is about half of Dickinson's algorithm, but the work of data preparation needs less operations only if the half bandwidth is below \(6\). For the special matrix tridiag\(\,(-1,2,-1)\) the suggested method of solution needs \(4n\) additions and one division.