This article aims to study the unconditional superconvergent behavior of nonconforming quadrilateral quasi-Wilson element for nonlinear Benjamin Bona Mahoney(BBM)equation.For the generalized rectangular meshes includi...This article aims to study the unconditional superconvergent behavior of nonconforming quadrilateral quasi-Wilson element for nonlinear Benjamin Bona Mahoney(BBM)equation.For the generalized rectangular meshes including rectangular mesh,deformed rectangular mesh and piecewise deformed rectangular mesh,by use of the special character of this element,that is,the conforming part(bilinear element)has high accuracy estimates on the generalized rectangular meshes and the consistency error can reach order O(h^(2)),one order higher than its interpolation error,the superconvergent estimates with respect to mesh size h are obtained in the broken H^(1)-norm for the semi-/fully-discrete schemes.A striking ingredient is that the restrictions between mesh size h and time stepτrequired in the previous works are removed.Finally,some numerical results are provided to confirm the theoretical analysis.展开更多
The orthogonal nonnegative matrix factorization （ONMF） has many applications in a variety of areas such as data mining, information processing and pattern recognition. In this paper, we propose a novel initializatio...The orthogonal nonnegative matrix factorization （ONMF） has many applications in a variety of areas such as data mining, information processing and pattern recognition. In this paper, we propose a novel initialization method for the ONMF based on the Lanczos bidiagonalization and the nonnegative approximation of rank one matrix. Numerical experiments are given to show that our initialization strategy is effective and efficient.展开更多
In this paper, we present a useful result on the structures of circulant inverse Mmatrices. It is shown that if the n × n nonnegative circulant matrix A = Circ[c0, c1,… , c（n- 1）] is not a positive matrix and ...In this paper, we present a useful result on the structures of circulant inverse Mmatrices. It is shown that if the n × n nonnegative circulant matrix A = Circ[c0, c1,… , c（n- 1）] is not a positive matrix and not equal to c0I, then A is an inverse M-matrix if and only if there exists a positive integer k, which is a proper factor of n, such that cjk 〉 0 for j=0,1…, [n-k/k], the other ci are zero and Circ[co, ck,… , c（n-k）] is an inverse M-matrix. The result is then extended to the so-called generalized circulant inverse M-matrices.展开更多
基金supported by the National Natural Science Foundation of China(No.11671105).
文摘This article aims to study the unconditional superconvergent behavior of nonconforming quadrilateral quasi-Wilson element for nonlinear Benjamin Bona Mahoney(BBM)equation.For the generalized rectangular meshes including rectangular mesh,deformed rectangular mesh and piecewise deformed rectangular mesh,by use of the special character of this element,that is,the conforming part(bilinear element)has high accuracy estimates on the generalized rectangular meshes and the consistency error can reach order O(h^(2)),one order higher than its interpolation error,the superconvergent estimates with respect to mesh size h are obtained in the broken H^(1)-norm for the semi-/fully-discrete schemes.A striking ingredient is that the restrictions between mesh size h and time stepτrequired in the previous works are removed.Finally,some numerical results are provided to confirm the theoretical analysis.
基金Acknowledgments. The work is supported by National Natural Science Foundation of China No. 10961010.
文摘The orthogonal nonnegative matrix factorization （ONMF） has many applications in a variety of areas such as data mining, information processing and pattern recognition. In this paper, we propose a novel initialization method for the ONMF based on the Lanczos bidiagonalization and the nonnegative approximation of rank one matrix. Numerical experiments are given to show that our initialization strategy is effective and efficient.
基金This work is supported by National Natural Science Foundation of China （No. 10531080）.
文摘In this paper, we present a useful result on the structures of circulant inverse Mmatrices. It is shown that if the n × n nonnegative circulant matrix A = Circ[c0, c1,… , c（n- 1）] is not a positive matrix and not equal to c0I, then A is an inverse M-matrix if and only if there exists a positive integer k, which is a proper factor of n, such that cjk 〉 0 for j=0,1…, [n-k/k], the other ci are zero and Circ[co, ck,… , c（n-k）] is an inverse M-matrix. The result is then extended to the so-called generalized circulant inverse M-matrices.
