A Cost-Effective Smoothed Multigrid with Modified Neighborhood-Based Aggregation for Markov Chains

Algorithm 5

Cost-effective SAM for Markov chains (CESAM), .

Input:

    : problem matrix,

    : iteration solution,

    , : pre and post relaxation steps.

Output:

    : iteration solution.

 (1) if not on the coarsest level then

 (2)   Relax  times.

 (3)  Construct according to (22).

 (4)  if in the first cycle then

 (5)   .

 (6)   Construct based on , and .

 (7)  else if    then

 (8)   .

 (9)  else

 (10)    .

 (11)   Construct based on , and .

 (12)   end if

 (13)   and .

 (14)   smooth , smooth .

 (15)   lumping , .

 (16)  

 (17)  

 (18)   Relax  times.

 (19) else

 (20)  the solution of , , by a direct solver.

 (21) end if

 (22) return  ;