A Normal Form Algorithm for Tensor Rank Decomposition

We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic of higher-order tensors subject to and genericity constraint. Reformulating this computational problem as system polynomial equations allows us leverage recent linear algebra tools from algebraic geometry. characterize complexity our in terms an property system—the multigraded regularity. prove effective bounds many formats ranks, which are independent interest overconstrained solving. Moreover, we conjecture general formula regularity, yielding (parameterized) time considered setting. Our experiments show that can outperform state-of-the-art algorithms by order magnitude accuracy, computation time, memory consumption.