Computing the UL factorisation by newton's method

Abstract

The U L if factorisation of symmetric banded Toeplitz matrices is obtained by solving a system of nonlinear equations. Due to the structure of the system it can be efficiently solved by a modified Gauss-Seidel algorithm which has super linear convergence. However, Newton's method with quadratic convergence is competitive. It is even more attractive because the Jacobian matrix is easy to obtain. When the matrix to be factorised is diagonally dominant then the Jacobian is also diagonally dominant and its inverse exists. However, a direct inversion is not desirable and a factorisation of the Newton iteration is proposed by the quadratic interlocking factorisation (QIF) method. Numerical results are compared to those obtained by a direct inversion (DI) and an LU factorisation. The influence of the starting point on the convergence is also studied.

Keywords:

• U L factorisation
• banded Toeplitz matrices
• Newton's method

C.R. CATEGORIES::

• G.1.3.
• G.1.5.

¹Institute Jozef Stefan, Ljubljana, Slovenia.

¹Institute Jozef Stefan, Ljubljana, Slovenia.

Notes

¹Institute Jozef Stefan, Ljubljana, Slovenia.