Development of the Block BiCGSTAB($\ell$) method for solving linear systems with multiple right hand sides

In this paper, we derive the Block BiCGSTAB($\ell$) method which is developed by extending the BiCGSTAB($\ell$) method. We also propose some techniques to improve convergence properties by applying orthogonalization and to improve the accuracy of the approximate solutions by additional matrix multiplications. Some numerical experiments indicate that the performance of the Block BiCGSTAB($\ell$) method with those stabilization techniques can be higher than that of the Block BiCGSTAB method.