A block version of Gmres, Bicg, Bicgstab for linear systems with multiple right-hand sides

systems with multiple right-hand side.

to the need to solve large linear systems.
All methods for solving linear systems can be divided into two classes: direct and iterative. Methods that lead to the solution for a finite number of arithmetic operations. Iterative methods are called, which should be obtained as a result of infinite repetition.
Many iterative methods are based on an iteration loop that accesses the coefficient matrix A once per loop and performs a matrix-vector multiply. To reduce data movement in the algorithm, our approach is to modify the algorithm such that more than one matrix-vector product occurs for a single memory access of A. To this end, we investigated alternatives for solving a single right-hand side system based on solving a corresponding block linear system AX = B, where X and B are both groups of vectors.