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In this article we consider the iterative schemes to compute the canonical(CP) approximation of quantized data generated by a function discretized on alarge uniform grid in an interval on the real line. This paper continues theresearch on the QTT method [16] developed for the tensor train (TT)approximation of the quantized images of function related data. In the QTTapproach the target vector of length $2^{L}$ is reshaped to a $L^{th}$ ordertensor with two entries in each mode (Quantized representation) and thenapproximated by the QTT tenor including $2r^2 L$ parameters, where $r$ is themaximal TT rank. In what follows, we consider the Alternating Least-Squares(ALS) iterative scheme to compute the rank-$r$ CP approximation of thequantized vectors, which requires only $2 r L\ll 2^L$ parameters for storage.In the earlier papers [17] such a representation was called Q$_{Can}$ format,while in this paper we abbreviate it as the QCP representation. We test the ALSalgorithm to calculate the QCP approximation on various functions, and in allcases we observed the exponential error decay in the QCP rank. The main ideafor recovering a discretized function in the rank-$r$ QCP format using thereduced number the functional samples, calculated only at $O(2rL)$ grid points,is presented. The special version of ALS scheme for solving the arisingminimization problem is described. This approach can be viewed as the sparseQCP-interpolation method that allows to recover all $2r L$ representationparameters of the rank-$r$ QCP tensor. Numerical examples show the efficiencyof the QCP-ALS type iteration and indicate the exponential convergence rate in$r$.

Quantized-CP Approximation and Sparse Tensor Interpolation of Function Generated Data