We propose a deflated CGW method (D-CGW) to approximate the solution of nonsymmetric positive definite linear systems. D-CGW utilizes some eigenspaces, and can be useful in cases when the slow convergence is due to a small number of eigenvalues with large magnitude in the generalized eigenvalue problem \(\textbf{S}\textbf{x}=\lambda \textbf{H} \textbf{x}\) , where \(\textbf{S}\) and \(\textbf{H}\) represent the skew-symmetric and symmetric parts of the coefficient matrix of nonsymmetric positive definite linear systems, respectively. Additionally, we introduce a skew-symmetric Lanczos method with deflated restarting, referred to as \(\hbox {S}^2\) Lan-DR, which simultaneously solves nonsymmetric positive definite linear systems and computes eigenspaces. The computed eigenspaces can be used in D-CGW to solve successive linear systems. Numerical experiments are given to illustrate the efficiency of the proposed methods.
