AN OVERVIEW OF APPROACHES FOR THE STABLE COMPUTATION OF HYBRID BICG METHODS

It is well known that BiCG can be adapted so that the operations with AT can be avoided, and hybrid methods with computational complexity al most similar to BiCG can be constructed in a further attempt to improv e the convergence behavior. Examples of this are CGS, Bi-CGSTAB, and B iCGstab(l). In many applications, the speed of convergence of these me thods is very dependent on the incorporated BiCG process. The accuracy of the iteration coefficients of BiCG depends on the particular choic e of the hybrid method. We will discuss the accuracy of these coeffici ents and how this affects the speed of convergence. We will show that hybrid methods exist which have better accuracy properties. This may l ead to faster convergence and more accurate approximations. We also di scuss look-ahead strategies for the determination of appropriate value s for I in BiCGstab(l). These strategies are easily applied for the hy brid part, in contrast to similar techniques for the BiCG part (but of course they do not solve the breakdown problems of the BiCG part).