Abstract
We consider a preconditioner of the MRTR method for solving a linear system of equations with real symmetric positive definite matrix. The proposed utilization of preconditioner has an advantage of preserving symmetric positive definiteness. The residual vector of MRTR method is the product of the starting residual vector γ0 and Hκ(A) only. Moreover the MRTR method is also based on the three-term recurrence formular of the CG method. Numerical experiments show effective convergence rate of the proposed preconditioning of the MRTR method as compared with the existing preconditioner.
