Solving large linear systems with multiple right-hand sides

In the present paper, we propose new variants of three block Krylov iterative methods for solving linear large systems with multiple right-hand sides. The first method is the block nonsymmetric Lanczos method, it allows us to solve the nonsymmetric linear systems. The second method is the block symmetric Lanczos method which allows us to solve the symmetric linear systems. For the third method, we derived a new procedure to generate a basis of matrix Krylov subspace and we developed a new Block symmetric Lanczos Method on the Normal Equations for solving the nonsymmetric linear systems. Finally, a few numerical examples are given to illustrate the effectiveness of the proposed methods.

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