Preconditioned Bi-conjugate Gradient Method of Large-scale Sparse Complex Linear Equation Group

In solving the large-scale sparse complex linear equation group, a lot of CPU operational time and computer memory is consumed to access zero elements of sparse coefficient matrix. As an effective solution, a fully-sparse storing scheme is proposed to store only nonzero elements of symmetrical part by chain pattern. For some ill-conditioned coefficient matrixes, iterative solution methods may incur such problems as slow convergence and even failure of convergence. Fortunately, some valid preconditioning techniques can improve the convergence by reducing condition number of ill-conditioned matrix. Based on a real incomplete Cholesky factorization preconditioner, we develop a fast convergent preconditioned Bi-conjugate gradient method (BCG) to solve the large-scale sparse complex linear equation group. Numerical experiments show that the new incomplete Cholesky factorization preconditioner accelerates the convergence and preconditioned bi-conjugate gradient method is available for the large-scale complex linear equation group.