In this paper,we propose a Quasi-Orthogonal Matching Pursuit(QOMP)algorithm for constructing a sparse approximation of functions in terms of expansion by orthonormal *** the two kinds of sampled data,data with noises ...
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In this paper,we propose a Quasi-Orthogonal Matching Pursuit(QOMP)algorithm for constructing a sparse approximation of functions in terms of expansion by orthonormal *** the two kinds of sampled data,data with noises and without noises,we apply the mutual coherence of measurement matrix to establish the convergence of the QOMP algorithm which can reconstruct s-sparse Legendre polynomials,Chebyshev polynomials and trigonometric polynomials in s step *** results are also extended to general bounded orthogonal system including tensor product of these three univariate orthogonal ***,numerical experiments will be presented to verify the effectiveness of the QOMP method.
Orthogonal matching pursuit(OMP for short)algorithm is a popular method of sparse signal recovery in compressed *** paper applies OMP to the sparse polynomial reconstruction *** from classical research methods using m...
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Orthogonal matching pursuit(OMP for short)algorithm is a popular method of sparse signal recovery in compressed *** paper applies OMP to the sparse polynomial reconstruction *** from classical research methods using mutual coherence or restricted isometry property of the measurement matrix,the recovery guarantee and the success probability of OMP are obtained directly by the greedy selection ratio and the probability *** results show that the failure probability of OMP given in this paper is exponential small with respect to the number of sampling *** addition,the recovery guarantee of OMP obtained through classical methods is lager than that of ℓ_(1)-minimization whatever the sparsity of sparse polynomials is,while the recovery guarantee given in this paper is roughly the same as that of ℓ_(1)-minimization when the sparsity is less than ***,the numerical experiments verify the availability of the theoretical results.
This paper is concerned with a piecewise smooth rational quasi-interpolation with algebraic accuracy of degree(n+1)to approximate the scattered data in R *** firstly use the modified Taylor expansion to expand the mea...
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This paper is concerned with a piecewise smooth rational quasi-interpolation with algebraic accuracy of degree(n+1)to approximate the scattered data in R *** firstly use the modified Taylor expansion to expand the mean value coordinates interpolation with algebraic accuracy of degree one to one with algebraic accuracy of degree(n+1).Then,based on the triangulation of the scattered nodes in R^(2),on each triangle a rational quasi-interpolation function is *** constructed rational quasi-interpolation is a linear combination of three different expanded mean value coordinates interpolations and it has algebraic accuracy of degree(n+1).By comparing accuracy,stability,and efficiency with the C^(1)-Tri-interpolation method of Goodman[16]and the MQ Shepard method,it is observed that our method has some computational advantages.
Taxonomy plays an important role in understanding the origin, evolution, and ecological functionality of biodiversity. There are large number of unknown species yet to be described by taxonomists, which together with ...
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Taxonomy plays an important role in understanding the origin, evolution, and ecological functionality of biodiversity. There are large number of unknown species yet to be described by taxonomists, which together with their ecosystem services cannot be effectively protected prior to description. Despite this, taxonomy has been increasingly underrated insufficient funds and permanent positions to retain young talents. Further, the impact factordriven evaluation systems in China exacerbate this downward trend, so alternative evaluation metrics are urgently necessary. When the current generation of outstanding taxonomists retires,there will be too few remaining taxonomists left to train the next generation. In light of these challenges, all co-authors worked together on this paper to analyze the current situation of taxonomy and put out a joint call for immediate actions to advance taxonomy in China.
The Cubic-Polynomial Interpolation scheme has been developed and applied to many practical ***,it seems the existing Cubic-Polynomial Interpolation scheme are restricted to uniform rectangular ***,this scheme has some...
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The Cubic-Polynomial Interpolation scheme has been developed and applied to many practical ***,it seems the existing Cubic-Polynomial Interpolation scheme are restricted to uniform rectangular ***,this scheme has some limitations to problems in irregular *** paper will extend the Cubic-Polynomial Interpolation scheme to triangular meshes by using some spline interpolation *** examples are provided to demonstrate the accuracy of the proposed schemes.
In this paper, by using multivariate divided differences to approximate the partial derivative and superposition, we extend the multivariate quasi-interpolation scheme based on dimension-splitting technique which can ...
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In this paper, by using multivariate divided differences to approximate the partial derivative and superposition, we extend the multivariate quasi-interpolation scheme based on dimension-splitting technique which can reproduce linear polynomials to the scheme quadric polynomials. Furthermore, we give the approximation error of the modified scheme. Our multivariate multiquadric quasi-interpolation scheme only requires information of lo- cation points but not that of the derivatives of approximated function. Finally, numerical experiments demonstrate that the approximation rate of our scheme is significantly im- proved which is consistent with the theoretical results.
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