A Symmetry Preserving Singular Value Decomposition

Singular value decomposition (SVD) is a general-purpose mathematical analysis tool that has been used in a variety of information-retrieval applications. As the size and complexity of retrieval collections increase, it is crucial for our analysis tools to scale accordingly. To this end, we have studied the application of a new theoretically justiied SVD approximation algorithm to the problem of...

In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...

in this paper, a numerical scheme for solving singular initial/boundary value problems presented.by applying the reproducing kernel hilbert space method (rkhsm) for solving these problems,this method obtained to approximated solution. numerical examples are given to demonstrate theaccuracy of the present method. the result obtained by the method and the exact solution are foundto be in good agr...

in this paper, he's highly proli c variational iteration method is applied ef-fectively for showing the existence, uniqueness and solving a class of singularsecond order two point boundary value problems. the process of nding solu-tion involves generation of a sequence of appropriate and approximate iterativesolution function equally likely to converge to the exact solution of the givenpr...

then σ is a singular value of A and u and v are corresponding left and right singular vectors, respectively. (For generality it is assumed that the matrices here are complex, although given these results, the analogs for real matrices are obvious.) If, for a given positive singular value, there are exactly t linearly independent corresponding right singular vectors and t linearly independent co...

Ren-Cang Li University of Texas at Arlington 15.1 Eigenvalue Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1 15.2 Singular Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-6 15.3 Polar Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-7 15.4 Generalized Eigenvalue Problems . . . . . . . . . . . . . . . . . . . 15-...

this article presents a new subspace-based technique for reducing the noise ofsignals in time-series. in the proposed approach, the signal is initially representedas a data matrix. then using singular value decomposition (svd), noisy datamatrix is divided into signal subspace and noise subspace. in this subspace division,each derivative of the singular values with respect to rank order is used ...