Linear homotopy method for computing generalized tensor eigenpairs

A homotopy method for computing the largest eigenvalue of an irreducible nonnegative tensor

“…In this situation, the Power-type methods can be slow. The algorithms proposed in this paper and in [6,7] show that the homotopy techniques are very useful for computing tensor eigenvalues. An interesting direction for future research is to apply a homotopy approach to compute extreme Z-eigenvalues for nonnegative tensors.…”

“…An attractive class of methods for solving polynomial systems is the homotopy continuation methods, see for example, [1,11,21]. Recently, the homotopy techniques have been successfully used to compute generalized eigenpairs of a tensor in [6,7]). However, the homotopy methods of [6,7] are not suitable for finding the Perron pair of a large size irreducible nonnegative tensor because those methods are designed to find all (real and complex) eigenpairs.…”

“…Recently, the homotopy techniques have been successfully used to compute generalized eigenpairs of a tensor in [6,7]). However, the homotopy methods of [6,7] are not suitable for finding the Perron pair of a large size irreducible nonnegative tensor because those methods are designed to find all (real and complex) eigenpairs. In this paper, we propose a homotopy method for computing the Perron pair of an irreducible nonnegative tensor.…”

Direct methods of B(D)-eigenpairs of tensors and application in diffusion kurtosis imaging

“…Chen et al in [4] proposed two homotopy continuation type algorithms to solve tensor eigenproblems. Chen et al in [5] proposed a linear homotopy method for computing generalized tensor eigenpairs and proved that this method finds all isolated B-eigenpairs.…”