Convergence properties of block GMRES and matrix polynomials

Block Iterative Methods and Recycling for Improved Scalability of Linear Solvers

“…p > 1, was the Conjugate Gradient method [32]. A first study of the Block GMRES was proposed in the thesis of Vital [33], followed by new theoretical results [17]. Plenty of applications of these methods have been proposed since then [34], [35], mainly for the simulation of wave propagation phenomena [36], [37] or lattice quantum chromodynamics [38] with multiple sources.…”

“…Still, numerous new or modified iterative methods have been developed to: pipeline reductions [9], [10], avoid synchronizations [11], [12], decrease the number of iterations by means of multiple search directions [13], [14] or Krylov subspace recycling [15], [16]. Iterative methods tailored to tackle efficiently problems with multiple right-hand sides have also blossomed [17]- [19]. Finally, it can also be beneficial to couple block methods and recycling [20], [21].…”

GMRES with multiple preconditioners

“…It was studied, e.g., in [9], [25], [34], [45], and applied recently, e.g., in [7]; see also [18] and references therein. We also mention block Arnoldi as a necessary important ingredient; see, e.g., [40], [41], [38, §6.12].…”

Short-Term Recurrence Krylov Subspace Methods for Nearly Hermitian Matrices

“…Thus, constructing an approximate solution to (1.1) requires s + 1 Hermitian solves. Methods for solving a Hermitian system with several right-hand sides (see, e.g., [11,17,24,29]) could potentially expedite this calculation.…”