This algorithm is useless without quantifying constants or numerically demonstrating that the constants are practical for some test problems. Although they cite

This algorithm is useless without quantifying constants or numerically demonstrating that the constants are practical for some test problems. Although they cite CMG in passing, they do not compare performance. They also (negligently) do not cite LAMG. MG algorithms are also highly parallelizable, which is not clearly the case for this algorithm. To get an idea of how essential it is to quantify constants, recall that in 1964, Fedorenko rigorously proved that the number of iterations of multigrid required to reduce the residual of Poisson on a rectangular grid with n points by a factor of epsilon is O(n * |log epsilon|). He quantified the associated constant as W(n, 0.01) <= 210000*n + W(10^6, 0.01) Groundbreaking optimal asymptotics, but utterly useless (the proposed algorithm had the wrong idea about good coarse spaces) and nobody cared until Achi Brandt came along it 1973 and revolutionized implicit solvers by demonstrated that if you get the details right W(n, discretization error) <= 40 * n (using only addition and shift operations).