swMATH ID: 14671
Software Authors: Chen, Liping; Han, Lixing; Zhou, Liangmin
Description: Computing tensor eigenvalues via homotopy methods. We introduce the concept of mode-k generalized eigenvalues and eigenvectors of a tensor and prove some properties of such eigenpairs. In particular, we derive an upper bound for the number of equivalence classes of generalized tensor eigenpairs using mixed volume. Based on this bound and the structures of tensor eigenvalue problems, we propose two homotopy continuation type algorithms to solve tensor eigenproblems. With proper implementation, these methods can find all equivalence classes of isolated generalized eigenpairs and some generalized eigenpairs contained in the positive dimensional components (if there are any). We also introduce an algorithm that combines a heuristic approach and a Newton homotopy method to extract real generalized eigenpairs from the found complex generalized eigenpairs. A MATLAB software package TenEig has been developed to implement these methods. Numerical results are presented to illustrate the effectiveness and efficiency of TenEig for computing complex or real generalized eigenpairs.
Homepage: http://users.math.msu.edu/users/chenlipi/teneig.html
Dependencies: Matlab
Related Software: TensorToolbox; PHCpack; Matlab; PHoM; HOM4PS; NACLab; Bertini; SPLATT; Algorithm 862; PHClab; MixedVol; libtropicana; Hom4PS-3; Gfan; PoSSo; DEMiCs; LAMG; Seigtool; Eigtool; ARPACK
Cited in: 30 Publications

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Computing tensor eigenvalues via homotopy methods. Zbl 1376.15017
Chen, Liping; Han, Lixing; Zhou, Liangmin

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