We propose general spectral and pseudo-spectral Jacobi-Galerkin methods for fractional order integro-differential equations of Volterra type. The fractional derivative is described in the Caputo sense. We provide rigo...
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We propose general spectral and pseudo-spectral Jacobi-Galerkin methods for fractional order integro-differential equations of Volterra type. The fractional derivative is described in the Caputo sense. We provide rigorous error analysis for spectral and pseudo-spectral Jacobi-Galerkin methods, which show that the errors of the approximate solution decay exponentially in $$L^\infty $$ norm and weighted $$L^2.$ -norm. The numerical examples are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]
The difference method for the space fractional coupled nonlinear Schr.6;dinger equations (CNLS) is studied. The fractional centered difference is used to approximate the space fractional Laplacian. This scheme cons...
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The difference method for the space fractional coupled nonlinear Schrödinger equations (CNLS) is studied. The fractional centered difference is used to approximate the space fractional Laplacian. This scheme conserves the discrete mass and energy. Due to the nonlocal nature of fractional Laplacian, in the classic Sobolev space, it is hard to obtain the error estimation in l ∞ . To overcome this difficulty, the fractional Sobolev space H α / 2.and a fractional norm equivalence in H α / 2.are introduced. Then the convergence of order O ( h 2.+ τ 2.) in l ∞ is proved by fractional Sobolev inequality, where h is the mesh size and τ is the time step. Numerical examples are given to illustrate the theoretical results at last.
A new first-order optimality condition for the basis pursuit denoise （BPDN） problem is derived. This condition provides a new approach to choose the penalty param- eters adaptively for a fixed point iteration algori...
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A new first-order optimality condition for the basis pursuit denoise （BPDN） problem is derived. This condition provides a new approach to choose the penalty param- eters adaptively for a fixed point iteration algorithm. Meanwhile, the result is extended to matrix completion which is a new field on the heel of the compressed sensing. The numerical experiments of sparse vector recovery and low-rank matrix completion show validity of the theoretic results.
A kind of equal-task multiple traveling salesman problem (ET-mTSP) was proposed based on the mTSP and its corresponding mathematical model was constructed;Then, a series of discrete operations for firefly algorithm (F...
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In this paper, applying majorization inequalities, new upper and lower bounds for summation of eigenvalues (including the trace) of the solution of the continuous algebraic Riccati equation are presented. Correspondin...
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There has been a growing interest in alignment-free methods for whole genome comparison and phylogenomic studies. In this study, we propose an alignment-free method for phylogenetic tree construction using whole-prote...
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There has been a growing interest in alignment-free methods for whole genome comparison and phylogenomic studies. In this study, we propose an alignment-free method for phylogenetic tree construction using whole-proteome sequences. Based on the inter-amino-acid distances, we first convert the whole-proteome sequences into inter-amino-acid distance vectors, which are called observed inter-amino-acid distance profiles. Then, we propose to use conditional geometric distribution profiles (the distributions of sequences where the amino acids are placed randomly and independently) as the reference distribution profiles. Last the relative deviation between the observed and reference distribution profiles is used to define a simple metric that reflects the phylogenetic relationships between whole-proteome sequences of different organisms. We name our method inter-amino-acid distances and conditional geometric distribution profiles (IAGDP). We evaluate our method on two data sets: the benchmark dataset including 2. genomes used in previous published papers, and another one including 67 mammal genomes. Our results demonstrate that the new method is useful and efficient.
The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can b...
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The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the 11 norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and ~hen the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.
In this paper, a linearly implicit conservative difference scheme for the coupled nonlinear Schr.6;dinger equations with space fractional derivative is proposed. This scheme conserves the mass and energy in the dis...
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In this paper,we propose a fast proximity point algorithm and apply it to total variation(TV)based image *** novel method is derived from the idea of establishing a general proximity point operator framework based on ...
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In this paper,we propose a fast proximity point algorithm and apply it to total variation(TV)based image *** novel method is derived from the idea of establishing a general proximity point operator framework based on which new first-order schemes for total variation(TV)based image restoration have been *** current algorithms for TV-based image restoration,such as Chambolle’s projection algorithm,the split Bregman algorithm,the Berm´udez-Moreno algorithm,the Jia-Zhao denoising algorithm,and the fixed point algorithm,can be viewed as special cases of the new first-order ***,the convergence of the new algorithm has been analyzed at ***,we make comparisons with the split Bregman algorithm which is one of the best algorithms for solving TV-based image restoration at *** experiments illustrate the efficiency of the proposed algorithms.
Complex networks have attracted much attention in diverse areas of science and technology. Multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and exper...
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