Purpose: a modified PCG method is used for solving a given system of linear equations

Input: A is a symmetric and positive definite coefficient matrix, b is the right-hand side vector, tol is the predermined tolerance, is the initial guess, is a SP-inverse parameter, and is the required inverse preconditioner

Output: x the solution vector.

Computational Procedure

Step 1: given ,ε_{P} SP-inverse parameter, inverse preconditioner