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In this paper we implement a numerical algorithm to compute codimension-one tori in threedimensional, volume-preserving maps. A torus is defined by its conjugacy to rigid rotation, which is in turn given by its Fourier series. The algorithm employs a quasi-Newton scheme to find the Fourier coefficients of a truncation of the series. We show that this method converges for tori of two example maps by continuation from an integrable case, and discuss the scaling of computational resources requireddoi:10.1137/15m1022859 fatcat:35o6vmlplnflrkzizq6c5j77ey