A Gaussian method for the square root of accretive operators
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In this work we consider the approximation of the inverse square root of regularly accretive operators in Hilbert spaces. Starting from a special integral formulation of the fractional power, we apply the Gauss-Legendre rule to obtain an approximation of rational type. We derive sharp error estimates, based on the use of the numerical range, which allow to a priori know the number of quadrature points necessary to achieve a prescribed accuracy. For practical purpose, we also analyze the behavior of the method in finite dimension, that is, in the case of bounded sectorial operators.