Development of the Shifted Block BiCGSTAB(l) Method and Improvement of Its Accuracy

Abstract

Abstract. In this paper, we develop the Shifted Block BiCGSTAB(ℓ) method for solving linear systems with multiple right hand sides and multiple shifts. This method is based on the Block BiCGSTAB(ℓ) method and the Shifted BiCGSTAB(ℓ) method. We also discuss the accuracy of the Shifted Block BiCGSTAB(ℓ) method and propose more accurate method. In numerical experiments, the Shifted Block BiCGSTAB(ℓ) method is faster than the Shifted BiCGSTAB(ℓ) method for each right hand side, although it’s accuracy is a little lower than the other in some cases.