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 , εP SP-inverse parameter, inverse preconditioner
Step 2: set
Step 3: solve , for y0
Step 4: set
Step 5: while
Step 6: compute a step length
Step 7: update the approximate solution
Step 8: update the residual
Step 9: solve
Step 10: compute a gradient correction factor
Step 11: set the new search direction
Step 12:
Step 13: end (while)
Algorithm 1: mEPCG ().