Abstract
The global BiCGSTAB (Gl-BiCGSTAB) method has been found to perform very well in many practical cases. However, like the BiCGSTAB method, it often converges slowly or stagnates for some non-symmetric linear systems with complex spectrum. In this paper, we propose a new global generalized product-type method based on the global BiCG (Gl-BCG) method to try and remedy these problems. To enhance stability of convergence and robustness, we also consider a variant of the new method based on minimization of the associate residual of F-norm and ascending order recurrence in place of reconstruction of the algorithm. Finally, numerical experiments are given to show that our methods can be more effective than the original methods.
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