An improvement in DS-BiCGstab(l) and its application for linear systems in lattice QCD

An improved algorithm of the DS-BiCGstab(l) method (IDSL) is proposed. The DS-BiCGstab(l) method (DSL) selects the value of l dynamically for the BiCGstab(l) method, but it does not always select a proper value for l in terms of its convergence. From this viewpoint, this research has focused on converging behavior with the BiCGstab(l) method, and the DSL has been improved. Several numerical results in lattice QCD show that this improvement leads dynamic selection of l to a value relevant to the convergence than the DSL without a substantial increase in the calculating costs.