Research Article

Approximating the Inverse of a Square Matrix with Application in Computation of the Moore-Penrose Inverse

Algorithm 2

Id = SparseArray i_, i_}  -> 1.}, {n, n ;
V = DiagonalMatrix@SparseArray 1/Normal Diagonal A ;
Do V1 = SparseArray V ;
   V2 = Chop A.V1 ; V3 = 3 Id + V2.(−3 Id + V2);
   V4 = SparseArray V2.V3 ;
   V = Chop −(1/4) V1.V3.SparseArray −13 Id
   + V4.(15 Id + V4.(−7 Id + V4)) ;
   Print V ;L i = N Norm Id − V.A, 1 ;
   Print "The residual norm is:"
    Column i}, Frame -> All, FrameStyle -> Directive Blue
    Column L i , Frame -> All, FrameStyle -> Directive Blue ;
   , {i, 1 ; // AbsoluteTiming