The　generalized　Roper-Suffridge　extension　operator　Phi(f)　on　the　bounded　complete　Reinhardt　domain　Omega　in　C-n　with　n　＞=　2　is　defined　by　[GRAPHICS]　requires　less　iterations　on　each　level,　especially　on　the　coarser　grids.　Many　operations　can　be　saved　in　the　new　cascadic　multigrid　algorithms.　The　main　ingredient　is　the　control　of　the　iteration　numbers　on　the　each　level　to　preserve　the　accuracy　without　over　iterations.　The　theoretical　justification　is　based　on　the　observations　that　the　error　reduction　rate　of　an　iteration　scheme　in　terms　of　the　smoothing　property　is　no　longer　accurate　while　the　iteration　number　is　big　enough.　A　new　formulae　of　the　error　reduction　rate　is　employed　in　our　new　algorithm.　Numerical　experiments　are　reported　to　support　our　theory.