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Multidimensional data smoothing has applications in signal and image processing, control, and other engineering disciplines. The two important data fitting criteria are the accuracy of the fit and the smoothness of the fit. In this paper, we discuss a tensor based algorithm for multidimensional smooth curve fitting where the cost function is a combination of two terms: one dealing with accuracy and the other one with the smoothness of the solution. We apply the proposed algorithm to digital color printer calibration in 1-d, 2-d and 3-d calibration techniques.