Scaled Fixed Point Algorithm for Computing the Matrix Square Root
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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.
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