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Description
The Canonical Polyadic (CP) decomposition is widely used to represent high-dimensional data in many applications, for example, solving high-dimensional PDEs like kinetic equations. A key challenge in these problems is the efficient estimation and reduction of the CP rank. The CP rank reduction task can be formulated as approximating the Khatri–Rao product of the CP factor matrices with a lower rank. We propose an approach based on the pivoted Cholesky decomposition to construct interpolative decompositions of the Khatri–Rao product. This method can serve as a standalone CP rank reduction technique or be integrated into classical optimization schemes such as CP-ALS. Moreover, the residuals produced at each step of the pivoted Cholesky naturally provide error indicators, enabling effective rank estimation. Preliminary numerical results demonstrate that this method achieves a balance between computational cost and approximation accuracy. Its effectiveness is further validated through applications to the Vlasov–Poisson equation.