Convergence acceleration of preconditioned conjugate gradient solver based on error vector sampling for a sequence of linear systems

In this article, we focus on solving a sequence of linear systems that have identical (or similar) coefficient matrices. For type problem, investigate subspace correction (SC) and deflation methods, which use an auxiliary matrix (subspace) to accelerate the convergence iterative method. practical simulations, these acceleration methods typically work well when range contains eigenspaces corresponding small eigenvalues matrix. We develop new algebraic construction method based error vector sampling in eigenvectors with are efficiently identified solution process. generated for following step. Numerical tests confirm both SC can process solver. Furthermore, examine applicability our technique estimation condition number also present algorithm preconditioned conjugate gradient estimation.