2020/02/18 by Harry F. Oviedo, Harry Oviedo, Hugo Lara +6
Computer Science · Mathematics · #65F30 #65H10 #65J15 #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #cs.NA #math.NA #msc:65F30 #msc:65H10 #msc:65J15
paper · pdf · doi:10.48550/arxiv.2002.08471
arxiv created 2020/02/18 · openalex publication_date 2020/02/18 · arxiv updated 2020/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.