Abstract: In this paper, we present a new interpolation formula of algebraic multigrid (AM G). The AMG algorithm with this formula can solve many problems, even very ill-conditioned problems like biharmonic equation and convection-diffusion equation with discontinuous coefficient etc. The theoretical analysis and numerical experiments demonstrate that this formula is very robust and efficient, so we have extended the application range of AMG.

Key words: algebraic multigrid, interpolation formula, linear system of equations