Reduction factor of multigrid iterations for elliptic problems

Multigrid method has been used widely to solve elliptic problems because of its applicability to many class of problems and fast convergence ([1], [3], [9], [10], [11], [12]). The estimate of convergence rate of multigrid is one of the main objectives of the multigrid analysis ([1], [2], [5], [6], [7], [8]). In many problems, the convergence rate depends on the regularity of the solutions([5], [6], [8]). In this paper, we present an improved estimate of reduction factor of multigrid iteration based on the proof in [6].