In this paper, we define the symmetric hyperdeterminant, eigenvalues and E-eigenvalues of a real supersymmetric tensor. We show that eigenvalues are roots of a one-dimensional polynomial, and whenâ€¦ (More)

The smoothing Newton method for solving a system of nonsmooth equations F (x) = 0, which may arise from the nonlinear complementarity problem, the variational inequality problem or other problems,â€¦ (More)

This paper studies the so-called bi-quadratic optimization over unit spheres min xâˆˆRn,yâˆˆRm âˆ‘ 1â‰¤i,kâ‰¤n, 1â‰¤j,lâ‰¤m bijklxiyjxkyl subject to â€–xâ€– = 1, â€–yâ€– = 1. We show that this problem is NP-hard and thereâ€¦ (More)

In this paper we take a new look at smoothing Newton methods for solving the nonlinear complementarity problem (NCP) and the box constrained variational inequalities (BVI). Instead of using anâ€¦ (More)

We consider superlinearly convergent analogues of Newton methods for nondifferentiable operator equations in function spaces. The superlinear convergence analysis of semismooth methods forâ€¦ (More)

The SNP500Cancer database provides sequence and genotype assay information for candidate SNPs useful in mapping complex diseases, such as cancer. The database is an integral component of the NCIâ€¦ (More)

MR diffusion kurtosis imaging (DKI) was proposed recently to study the deviation of water diffusion from Gaussian distribution. Mean kurtosis, the directionally averaged kurtosis, has been shown toâ€¦ (More)