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The canonical polyadic decomposition is one of the most used tensor decomposition. However classical decomposition algorithms such as alternating least squares suffer from convergence problems and thus the decomposition of large tensors can be very time consuming. Recently it has been shown that the decomposition can be rewritten as a joint eigenvalue decomposition problem. In this paper we propose a fast joint eigenvalue decomposition algorithm then we show how it can benefit the canonical polyadic decomposition of large tensors.