DOI: 10.24193/fpt-ro.2023.1.16

Authors: Harry Oviedo, Hugo Lara and Oscar Dalmau

Abstract: 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 - X² = 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.

Key Words and Phrases: Matrix square root, fixed point algorithm, matrix iteration and geometric optimization.

2010 Mathematics Subject Classification: 65J15, 65F45, 65H10.

Published on-line: February 1st, 2023.

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