A Block Seed Method For Solving Linear Systems With Multiple Right-hand Sides

In this paper, we consider the seed projection method for solving linear systems with multipleright-hand sides. To improve the convergence rate of the method, we combine the block GMRESmethod and the seed projection method and propose the block seed method, Moreover, in order toaccelerate the convergence, we analyze the two seed-selection approaches, and study the residualproperties of the algorithms. The experimental result indicated that the newly proposed algorithms aresuperior to seed projection method.In order to solve complex symmetric linear systems with multiple right-hand sides, the realvalued MINRES seed projection method and real valued block MINRES seed projection method areproposed by transforming them into real symmetric linear systems with multiple right-hand sides. Thenumerical results show that the proposed methods are effective.