  This paper addresses the numerical solution of the matrix square root
problem. Two fixed point iterations are proposed by rearranging the nonlinear
matrix equation $A - X^2 = 0$ and incorporating a positive scaling parameter.
The proposals only need to compute one matrix inverse and at most two matrix
multiplications per iteration. A global convergence result is established. The
numerical comparisons versus some existing methods from the literature, on
several test problems, demonstrate the efficiency and effectiveness of our
proposals.
