The aor method for preconditioned linear systems^†

^† This work was supported by Fundação Calouste Gulbenkian and Instituto de Telecomunicaç[otilde]es de Coimbra.

Abstract

In this paper we analyse the behaviour of the rate of convergence of the Accelerated Overrelaxation (AOR) method when the linear system Ax = b is preconditioned by performing certain elementary row operations on A or by a single Gauss-Jordan elimination. Under some assumptions we prove that the AOR method applied to the preconditioned systems gives improvements in the rate of convergence.

Keywords:

• Linear system
• iterative method
• preconditioned linear system
• Accelerated Overrelaxation (AOR) method

^† This work was supported by Fundação Calouste Gulbenkian and Instituto de Telecomunicaç[otilde]es de Coimbra.

^† This work was supported by Fundação Calouste Gulbenkian and Instituto de Telecomunicaç[otilde]es de Coimbra.

Notes

^† This work was supported by Fundação Calouste Gulbenkian and Instituto de Telecomunicaç[otilde]es de Coimbra.