Aitken extrapolation method for computing the largest eigenvalue of nonnegative tensors

Tensor eigenvalue problem recently attracts much research interest since it plays a very important role in both theoretical analysis of multilinear algebra and many practical applications. Numerical iterative schemes were proposed to calculate the maximum eigenvalue of a non-negative tensor based on a Perron-Frobenius theorems. Using Aitken extrapolation technique, we propose a class of new iterative methods to calculate the largest eigenvalue of irreducible nonnegative tensors. The implementation of Aitken extrapolation is well studied. Numerical experiments show that the new methods are feasible and faster than original approaches.