In this paper, a homotopy continuation method for the computation of nonnegative Z-/H-eigenpairs of a nonnegative tensor is presented. We show that the homotopy continuation method is guaranteed to compute a nonnegative eigenpair. Additionally, using degree analysis, we show that the number of positive Z-eigenpairs of an irreducible nonnegative tensor is odd. A novel homotopy continuation method is proposed to compute an odd number of positive Z-eigenpairs, and some numerical results are presented.

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In this paper, we analyze the Bregman iterative model using the G-norm. Firstly, we show the convergence of the iterative model. Secondly, using the source condition and the symmetric Bregman distance, we consider the error estimations between the iterates and the exact image both in the case of clean and noisy data. The results show that the Bregman iterative model using the G-norm has the similar good properties as the Bregman iterative model using the L2-norm.

A new Tikhonov regularization method of Fuhry and Reichel [A new Tikhonov regularization method, Numerical Algorithms, 59:433-445, 2011] exhibits the excellent properties for ill-posed problems, but it can only deal with small or moderate size problems because of the expensive computation of singular value decomposition (SVD). In this paper, we extend the above new Tikhonov regularization method to solve large-scale problems, e.g., image restoration problem with periodic boundary conditions, and realize this extending by applying Fast Fourier Transformation (FFT) algorithm to the spectral decomposition of the block circulant with circulant blocks (BCCB) matrices. Experimental results confirm the superiority of our new method.