Abstract :
In this paper a new iterative method which is a hybrid of the BiCGSTAB and GPBiCG methods is proposed. The present method is an extension of the BiCGSTAB2 method. In the BiCGSTAB2 method which is a hybrid type method, two parameters of the BiCGSTAB method are adopted at even iteration step, and those of the GPBiCG method are used at odd iteration step. In the present GPBiCG(m,ℓ) method, parameters of the BiCGSTAB method are adopted at consecutive m iteration steps, and afterwards those of the GPBiCG method are also utilized in succession at ℓ iteration steps. We will examine the convergence property of the GPBiCG(m,ℓ) method and investigate its effectiveness through numerical experiments.
