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Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials(Elsevier BV, 2015-06-07)We show that a weighted least squares approximation of q-Bézier coefficients provides the best polynomial degree reduction in the q-L2-norm. We also provide a finite analogue of this result with respect to finite q-lattices and we present applications of these results to q-orthogonal polynomials. © 2015 Elsevier Inc. All rights reserved.