A fast algorithm for solving a Toeplitz system
The author derives a fast algorithm for solving symmetric penta-diagonal systems. The Toeplitz \(n \times n\) matrix \(A\) of the system of linear algebraic equations is decomposed. The Sherman-Morison-Woodbury formula is used to obtain conditions under which the matrix \(A\) is invertible. Quite complicated formulas lead to a fast algorithm for solving the original system. The author proves that for strictly diagonally dominant \(A\) the algorithm is stable and works well. Two numerical examples illustrate the theory.
symmetric penta-diagonal systems of linear algebraic equations
fast direct algorithm for finding a solution
scientific article; zbMATH DE number 5817279