A note on the SSOR convergence domain due to Neumaier and Varga

Abstract

In a recent paper A. Neumaier and R. S. Varga show that if A is an n ×ncomplex H-matrix with 12 <ϱ(∣JA∣) < 1, then ϱ(SAω) < 1 for all 0 < ω <g̃w:=2/ (1 + √2ϱ(∣JA∣) − 1), where SAω and JA are, respectively, the symmetric successive overrelaxation (SSOR) iteration matrix and the Jacobi iteration matrix associated with A. We show that ϱ(SAg̃w) < 1. This allows us to also sharpen further results on the SSOR method for H-matrices due to Varga, Niethammer, and Cai.