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Summary In this paper, we consider efficient algorithms for solving the algebraic equation Aαboldu=boldf, 0<α<1, where scriptA is a properly scaled symmetric and positive definite matrix obtained from finite difference or finite element approximations of second‐order elliptic problems in Rd, d=1,2,3. This solution is then written as boldu=Aβ−αboldF with boldF=A−βboldf with β positive integer. The approximate solution method we propose and study is based on the best uniform rational approximation of the function tβ−α for 0

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