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This paper is concerned with improving the empirical convergence speed of block‐coordinate descent algorithms for approximate nonnegative tensor factorization (NTF). We propose an extrapolation strategy in‐between block updates, referred to as heuristic extrapolation with restarts (HER). HER significantly accelerates the empirical convergence speed of most existing block‐coordinate algorithms for NTF, in particular for challenging computational scenarios, while requiring a negligible additional computational budget. [ABSTRACT FROM AUTHOR]