Absolute Diagonal Scaling Preconditioner of COCG Method for Symmetric Complex Matrix

Abstract

The iterative method, i.e., Conjugate Orthogonal Conjugate Gradient (COCG) method included in the Krylov Subspace methods, can solve a linear system of equations Ax = b. This COCG method is well known to solve by the system with large sparse matrix arises for realistic problems by FEM. The characteristic of the matrix is that the diagonal entries only are complex besides real nondiagonal entries. In this paper, we propose new preconditioner for a matrix with complex diagonal entries only and real nondiagonal entries. We refer to as an absolute diagonal scaling (A-D-s) technique. This method can reduce computation times and amount of memory compared with nondiagonal scaling method.