Finding the Largest Eigenvalue of a Nonnegative Tensor

By Michael Kwok-Po Ng, Liqun Qi, Guanglu Zhou. SIAM Journal on Matrix Analysis and Applications, 2009

354 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/b1d097883e9e84f4d645dc8ae28754093a0a3006

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Citations in the corpus

Essentially Positive Tensors (2010, methodology): “This author conjectures that the iterative method for calculating the largest eigenvalue of an irreducible nonnegative tensor, which is an extension of a method of Collatz, proposed in [6] will converge to the largest eigenvalue if the tensor satisfies Theorem 3.”
On the spectrum of hypergraphs (2017, background): “Various properties of eigenvalues of a tensor have been studied in [7, 8, 21, 27, 34, 35, 38, 39].”
Singular values of a real rectangular tensor (2010, methodology): “Applications of eigenvalues of square tensors include medical resonance imaging [1, 19], higher-order Markov chains [12], positive definiteness of even-order multivariate forms in automatical control [13], and best-rank one approximation in data analysis [18], etc.”
On the limiting probability distribution of a transition probability tensor (2014, background): “Numerical results in Table 4 given in [19] have shown that λ0 is not equal to 1.”
Shifted Power Method for Computing Tensor Eigenpairs (2010, background): “Tensor eigenvalues and eigenvectors have received much attention lately in the literature [13, 18, 20, 19, 4, 15, 27].”
Perron–Frobenius theorem for nonnegative multilinear forms and extensions (2009, neutral): “The sequence produced by the present power algorithm can be seen to coincide with the one of [7], up to a normalization factor, and therefore, the present results imply that the algorithm of [7] does converge, under the weak primitivity condition.”
H$^+$-Eigenvalues of Laplacian and Signless Laplacian Tensors (2013, methodology): “There is a rich theory on eigenvalues of a nonnegative tensor [4, 5, 8, 17, 18, 27, 28].”
Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging (2013, background): “Eigenvalue decomposition for tensors means different things to different researchers (see [12] [16] [18] [19], for example).”
M-tensors and nonsingular M-tensors (2013, background): “Introduction Several topics in multi-linear algebra have attracted considerable attention in recent years, especially on the eigenvalues of tensors [11–14] and higher order tensor decompositions [10].”
A new eigenvalue inclusion set for tensors and its applications (2015, background): “Recently, tensor eigenvalues and eigenvectors have received much attention in the literature [1,8,9,11,15,18–22,25].”
An S-type eigenvalue localization set for tensors (2015, background): “Introduction Eigenvalue problems of tensors have become an important topic of study in numerical multilinear algebra, and they have a wide range of practical applications; see [2, 3, 4, 5, 7, 8, 9, 10, 11, 17, 18, 19, 21, 22, 24, 25].”
M-Tensors and Some Applications (2014, neutral): “In particular, theory of, and algorithms for calculating, eigenvalues of nonnegative tensors are well developed [6, 7, 8, 12, 16, 18, 19, 23, 26, 27, 28].”