“…Instead of applying shifted Krylov subspace methods to the solution of each of the p multi-shifted linear systems independently [13][14][15][16][17][18][19][20], or block Krylov subspace methods to the solution of the L linear systems with multiple right-hand sides in sequence [10,12,21,22], it is much more efficient to use a shifted block method to solve all of the multi-shifted linear systems simultaneously [23,24]. In this context we refer to the system (A − σ 1 I)X 1 = B as the base shifted block system, and to (A − σ i I)X i = B (i = 2, .…”