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

Algorithm 1

SAM method for Markov chain (V cycle), SAM.

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 .

 (4)   and .

 (5)    ← smooth , smooth .

 (6)    ← lumping , .

 (7)  

 (8)  .

 (9)    ← Relax()  times.

 (10) else

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

 (12) end if

 (13) return  ;