BiCR-type methods for families of shifted linear systems

The shifted linear systems with non-Hermitian matrices often arise from the numerical solutions for time-dependent PDEs, computing the large-scale eigenvalue problems, control theory and so on. In the present paper, we develop two shifted variants of BiCR-type methods for solving such linear systems. These variants of BiCR-type methods take advantage of the shifted structure, so that the number of matrix–vector multiplications and the number of inner products are the same as a single linear system. Finally, extensive numerical examples are reported to illustrate the performance and effectiveness of the proposed methods.