The Scientific World Journal / 2013 / Article / Alg 3

Research Article

A Higher Order Iterative Method for Computing the Drazin Inverse

Algorithm 3

PM X_   :=
With Id = SparseArray i_, i_}  -> 1.}, {n, n ,
       X1 = A.X; X2 = −7 Id + X1.(9 Id + X1.(−5 Id + X1)); X3 = X1.X2;
       (−1/8) X.X2.(12 Id + X3.(6 Id + X3))
          ;
InitialMatrix A_   := 1/SingularValueList A, 1 [1   ConjugateTranspose A ;
InitialDrazin A_   := 2/Tr MatrixPower A, k + 1   MatrixPower A, k ;
DrazinInverse A_, tolerance_   := If k == 0,
      Module X0 = InitialMatrix A , FixedPoint (PM #   &), X0,
      SameTest -> (Norm #1 - #2, Infinity   <= tolerance  &) ,
      Module X0 = InitialDrazin A , FixedPoint (PM #   &), X0,
      SameTest -> (Norm #1   #2, Infinity   <= tolerance  &)
      ;

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