The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenva...The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.展开更多
A preconditioning method for the finite element stiffness matrix is given in this paper. The triangulation is refined in a subregion; the preconditioning process is composed of resolution of two regular subproblems; t...A preconditioning method for the finite element stiffness matrix is given in this paper. The triangulation is refined in a subregion; the preconditioning process is composed of resolution of two regular subproblems; the condition number of the preconditioned matrix is 0(1 + log H/h), where H and h are mesh sizes of the unrefined and local refined triangulations respectively.展开更多
现有的非负矩阵分解方法往往聚焦于数据全局结构信息的学习,在很多情况下忽略了对数据局部信息的学习,而局部学习的方法也通常局限于流行学习,存在一些缺陷。为解决这一问题,提出了一种基于数据局部相似性学习的鲁棒非负矩阵分解算法(Ro...现有的非负矩阵分解方法往往聚焦于数据全局结构信息的学习,在很多情况下忽略了对数据局部信息的学习,而局部学习的方法也通常局限于流行学习,存在一些缺陷。为解决这一问题,提出了一种基于数据局部相似性学习的鲁棒非负矩阵分解算法(Robust nonnegative matrix factorization with local similarity learning,RLS-NMF)。采用一种新的数据局部相似性学习方法,它与流形方法存在显著区别,能够同时学习数据的全局结构信息,从而能挖掘数据类内相似和类间相离的性质。同时,考虑到现实应用中的数据存在异常值和噪声,该算法还使用l_(2,1)范数拟合特征残差,过滤冗余的噪声信息,保证了算法的鲁棒性。多个基准数据集上的实验结果显示了该算法的最优性能,进一步证明了该算法的有效性。展开更多
文摘The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.
文摘A preconditioning method for the finite element stiffness matrix is given in this paper. The triangulation is refined in a subregion; the preconditioning process is composed of resolution of two regular subproblems; the condition number of the preconditioned matrix is 0(1 + log H/h), where H and h are mesh sizes of the unrefined and local refined triangulations respectively.
文摘现有的非负矩阵分解方法往往聚焦于数据全局结构信息的学习,在很多情况下忽略了对数据局部信息的学习,而局部学习的方法也通常局限于流行学习,存在一些缺陷。为解决这一问题,提出了一种基于数据局部相似性学习的鲁棒非负矩阵分解算法(Robust nonnegative matrix factorization with local similarity learning,RLS-NMF)。采用一种新的数据局部相似性学习方法,它与流形方法存在显著区别,能够同时学习数据的全局结构信息,从而能挖掘数据类内相似和类间相离的性质。同时,考虑到现实应用中的数据存在异常值和噪声,该算法还使用l_(2,1)范数拟合特征残差,过滤冗余的噪声信息,保证了算法的鲁棒性。多个基准数据集上的实验结果显示了该算法的最优性能,进一步证明了该算法的有效性。
