The computation of the Moore-Penrose inverse and Drazin inverse of real matrix can be transformed into solving the problem of linear matrix equations. Then the modified conjugate gradient method can be used to get the general solution of linear matrix equations. Finally, the Moore-Penrose inverse and Drazin inverse of real matrix can be obtained directly or through matrix multiplication. The modified conjugate gradient method is different from the usual conjugate gradient method. It which does not require the positive definite, reversible or full column rank of the coefficient matrix of the involved linear algebraic equations. Thus this method is always feasible. The numerical experiments show that the algorithm is effective.
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