The Multigrid methods are interactive methods of linear systems resolution, therefore, strongly dependent of the initial estimate attributed to the incognita of the problem. 

The great differentials of the methods Multigrid in relation to other interactive methods is that it solves linear systems of different sizes to improve the initial estimate attributed to the incognita of the problem. This group of operations can be interpreted as a pre-processing stage of the linear system, making that the solver executes a smaller number of iterations to reach the convergence criterion specified for the original linear system. 

The principals The way as these linear systems of different sizes links with the original system is that characterizes the different Multigrid solver types.