The CANDECOMP/PARAFAC (CP) decomposition is a generalization of the spectral matrices to higher-order tensors. In this paper we use CP study unitary equivalence higher order tensors and construct several invariants local for general Based on new method, coefficient 3-qubit states obtain necessary sufficient criterion tripartite in terms decomposition. We also generalize method some multi-partit...

As the consumption of Chinese medicine resources increases, waste traditional extraction cannot be disposed reasonably, which has a serious impact on environment. Dissolved organic matter (DOM), crucial fraction in herbal residue, can bond to heavy metals (HMs), creating potential environmental risk. This study investigated binding property residue DOM with Cu(II) via two-dimensional Fourier tr...

This paper presents a Cramér-Rao lower bound (CRLB) on the variance of unbiased estimates of factor matrices in Canonical Polyadic (CP) or CANDECOMP/PARAFAC (CP) decompositions of a tensor from noisy observations, (i.e., the tensor plus a random Gaussian i.i.d. tensor). A novel expression is derived for a bound on the mean square angular error of factors along a selected dimension of a tensor o...

The damped Gauss-Newton (dGN) algorithm for CANDECOMP/PARAFAC (CP) decomposition can handle the challenges of collinearity of factors and different magnitudes of factors; nevertheless, for factorization of an N-D tensor of size I1 × · · · × IN with rank R, the algorithm is computationally demanding due to construction of large approximate Hessian of size (RT × RT ) and its inversion where T = n...

We consider the line spectral estimation problem which aims to recover a mixture of complex sinusoids from a small number of randomly observed time domain samples. Compressed sensing methods formulates line spectral estimation as a sparse signal recovery problem by discretizing the continuous frequency parameter space into a finite set of grid points. Discretization, however, inevitably incurs ...