Parallel implementation of an iterative algorithm for solving nonsymmetric linear systems with partial retention of spectral/singular information on explicit restarts

A parallel implementation of the SOFGMRES(m) iterative algorithm with partial retention of information on explicit restarts is discussed. An arbitrary initial subspace is an important degree of freedom for this algorithm. From the convergence substantiation of the SOFGMRES(m) algorithm it follows that an appropriately chosen initial subspace can be considered as an additional preconditioner, since this subspace reduces the generalized condition number of a matrix and accelerates the convergence of the SOFGMRES(m) algorithm. The numerical results show the reliability of the proposed algorithm and its algebraic and parallel efficiency compared to the classical Krylov subspace-type algorithms.