Stein-rosenberg type theorems for the ssor and ussor, psd and mpsd methods

Abstract

In this paper we first prove the comparison theorems for generalized iteration matrices associated with the SSOR and USSOR iterative methods, and, as consequences, we give a set of Stein-Rosenberg type theorems for the SSOR and USSOR, the PSD and MPSD methods, extending the previous existing results. Finally we point out that the above set of these theorems are valid for the generalized SSOR and USSOR, and the generalized PSD and MPSD iterative methods.

Keywords:

• Stein-Rosenberg type theorem
• SSOR method
• USSOR method
• PSD method
• MPSD method
• generalized preconditioned iterative methods

C.R.Categories:

• G1.3