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On determinants and eigenvalue theory of tensors
We investigate properties of the determinants of tensors, and their applications in the eigenvalue theory of tensors. We show that the determinant inherits many properties of the determinant of aExpand
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The Laplacian of a uniform hypergraph
  • S. Hu, L. Qi
  • Computer Science, Mathematics
  • J. Comb. Optim.
  • 1 February 2015
Abstract In this paper, we investigate the Laplacian, i.e., the normalized Laplacian tensor of a $$k$$-uniform hypergraph. We show that the real parts of all the eigenvalues of the Laplacian are inExpand
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The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph
  • S. Hu, L. Qi
  • Mathematics, Computer Science
  • Discret. Appl. Math.
  • 1 May 2014
In this paper, we show that the eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a k-uniform hypergraph are closely related to some configuredExpand
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Finding the extreme Z-eigenvalues of tensors via a sequential semidefinite programming method
  • S. Hu, Z. Huang, L. Qi
  • Mathematics, Computer Science
  • Numer. Linear Algebra Appl.
  • 1 December 2013
SUMMARY In this paper, we first introduce the tensor conic linear programming (TCLP), which is a generalization of the space TCLP. Then an approximation method, by using a sequence of semidefiniteExpand
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Error Bounds for the Solution Sets of Quadratic Complementarity Problems
In this article, two types of fractional local error bounds for quadratic complementarity problems are established, one is based on the natural residual function and the other on the standardExpand
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A generalized Newton method for absolute value equations associated with second order cones
In this paper, we introduce the absolute value equations associated with second order cones (SOCAVE in short), which is a generalization of the absolute value equations discussed recently in theExpand
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Finding the Maximum Eigenvalue of Essentially Nonnegative Symmetric Tensors via Sum of Squares Programming
Finding the maximum eigenvalue of a tensor is an important topic in tensor computation and multilinear algebra. Recently, for a tensor with nonnegative entries (which we refer it as a nonnegativeExpand
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An iterative algorithm for third-order tensor multi-rank minimization
Recent work by Kilmer et al. (A third-order generalization of the matrix SVD as a product of third-order tensors, Department of Computer Science, Tufts University, Medford, MA, 2008; Linear AlgebraExpand
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A Tensor Analogy of Yuan’s Theorem of the Alternative and Polynomial Optimization with Sign structure
  • S. Hu, G. Li, L. Qi
  • Computer Science, Mathematics
  • J. Optim. Theory Appl.
  • 9 July 2014
Yuan’s theorem of the alternative is an important theoretical tool in optimization, which provides a checkable certificate for the infeasibility of a strict inequality system involving twoExpand
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Theorems of the Alternative for Inequality Systems of Real Polynomials
  • S. Hu, Z. Huang
  • Computer Science, Mathematics
  • J. Optim. Theory Appl.
  • 7 February 2012
In this paper, we establish theorems of the alternative for inequality systems of real polynomials. For the real quadratic inequality system, we present two new results on the matrix decomposition,Expand
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