Abstract
Linear systems with multiple right-hand sides arise in many applications such as lattice quantum chromodynamics (QCD) calculation, the eigensolver using contour integral, and so on. Although the direct solvers are effective for solving the systems, it is difficult to apply them when the problem size is very large. Block Krylov subspace methods have been proposed as efficient numerical methods for solving the systems. In this paper, we describe the several Block Krylov subspace methods. After that, the cause of the deterioration of the accuracy of approximate solutions generated by the Block BiCGSTAB method is analyzed, and the Block BiCGGR method for computing high accuracy solutions is described.
