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We consider the eigenvalue problem of a class of non-compact linear operators given as the sum of a multiplication and a integral operators. A product integration method is used to approximation based on numerical integration of the weakly singular kernel integral operator. It is shown that entries of the corresponding matrix of this method can be evaluated exactly. The convergence of the method is...
In this paper, we consider group consensus problem by giving a kind of new protocol in which communication graph weights are all nonnegative. This is also consistent with classic protocols. The sufficient conditions which group consensus under this kind of protocols can reach for both single and second order multi-agent system are obtained. Finally, numerical examples are given to illustrate our theoretical...
In this paper, the impact of edge-adding probability on both synchronizability and average path length of Klein berg small world networks is investigated. It could be seen from the analysis that two dimensional Klein berg small world networks have similar properties as NW small world networks but Klein berg small world network is more general, that is, the synchronizability becomes stronger as the...
The Laplacian matrix is the difference of the diagonal matrix of vertex degrees and the adjacency matrix of a graph G. In this paper, we first give two sharp upper bounds for the radius of the Laplacian spectrum of G in terms of the edge number, the vertex number, the largest degree, the second largest degree and the smallest degree of G by applying non-negative matrix theory and graph theory. Then,...
When denoising with the method of Weickert's an isotropic diffusion equation, the textures and details will be compromised. A fidelity term is added into Weickert's equation. The coefficient of fidelity term will vary adaptively with the instant image, which makes that the diffusion term and the fidelity term come to a better compromise. Otherwise, when deciding the edge directions, because of the...
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