Preconditioned Bi-conjugate Gradient Method of large-scale complex linear equations

Bi-conjugate gradient method (BCG) has potential problems on slow convergence or divergence when complex linear equations are large-scale or coefficient matrix of complex linear equations is ill. Fortunately, appropriate preconditioning techniques can speed convergence by reducing condition number of ill matrix. Based on a real incomplete Cholesky decomposition preconditioner, a preconditioned method for complex linear equations is built in this paper, and then a preconditioned bi-conjugate gradient method (PBCG) is obtained by combining the preconditioner and bi-conjugate gradient method. Numerical examples show that the preconditioned bi-conjugate gradient method is speedy, high-performance and applicable to solve system of large-scale complex linear equations.