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Stochastic analytic continuation is an excellent numerical method for analytically continuing Greens functions from imaginary frequencies to real frequencies,although it requires significantly more computational time than the traditional MaxEnt method.We develop an alteate implementation of stochastic analytic continuation which expands the dimensionless field n(x) introduced by Beach using orthogonal polynomials.We use the keel polynomial method (KPM) to control the Gibbs oscillations associated with truncation of the expansion in orthogonal polynomials.Our KPM variant of stochastic analytic continuation delivers improved precision at a significantly reduced computational cost.