Multi-parameter HSS Preconditioning Method For Weighted Toeplitz Regularized Least Squares Computation Squares Problems

In many real applications,such as image processing,we need to solve a class of weighted Toeplitz regularized least square problems.As well know,the Krylov subspace methods are good choices for solving this kind of problems.To further improve the convergence rate of the Krylov subspace methods,a kind of multi-parameter Hermitian and Skew-Hermitian splitting(HSS)preconditioner is proposed based on the HSS preconditioner.Comparing with the original HSS preconditioner,the new preconditioner is very flexibly since it has more than one parameters.However,how to choose the optimal values of parameters is a tough task.In this paper,a kind of the optimal parameter values is defined by minimizing the Frobenius norm of the difference of the coefficient matrix and the preconditioner.Furthermore,a practical and easily computed formula for computing these optimal parameter values is proposed.Numerical experiments show that the proposed preconditioner with the parameter values are computed by using this practical formula is efficient and robust in speeding up the Krylov subspace methods for solving weighted Toeplitz regularized least square problems.