Restrictively Preconditioned Conjugate Gradient Method For Weighted Toeplitz Regularized Least-squares Problems

Bai Zhongzhi et al.(IMA J.Numer.Anal.,23(2003))proposed a restrictively preconditioned conjugate gradient(RPCG)methods for solving a linear system with a two-by-two structure.This method includes classical Krylov subspace iteration methods such as conjugate gradient method and conjugate residual method,CGNR,CGNE,and has wide versatility.Aiming at the weighted Toeplitz regularized least squares problem,this paper proposes a new preconditioned matrix based on the restrictively precondi-tioned conjugate gradient method.The spectral distribution of the new preprocessing matrix is theoretically analyzed and the convergence of the new preprocessing conjugate gradient method is obtained.Furthermore,the experimental data shows that the new preprocessed conjugate gradient method has good numerical performance for solving the weighted Toeplitz least squares problem...