A note on the upper bound in SA AMG convergence analysis

In M. Brezina, P. Vaněk and P. S. Vassilevski, An improved convergence of smoothed aggregation algebraic multigrid, Numer. Linear Algebra Appl., 19 (2012), pp. 441–469], a uniform convergence bound for smoothed aggregation algebraic multigrid with aggressive coarsening and massive polynomial prolongator and multigrid smoothers is established provided that the number of smoothing steps is equal to the coarsening ratio parameter ν. The final convergence estimate needs the uniform bound for the constant C_ν ∕ (2ν + 1). In this note, we give an improved upper bound. Copyright © 2013 John Wiley & Sons, Ltd.