We propose a theory of eigenvalues, eigenvectors, singular values, and singular vectors for tensors based on a constrained variational approach much like the Rayleigh quotient for symmetric matrix eigenvalues. These notions are particularly useful in generalizing certain areas where the spectral theory of matrices has traditionally played an important role. For illustration, we will discuss a m...

This technical report introduces some software packages for partial SVD computation, including optimized PROPACK, modified PROPACK for computing singular values above a threshold and the corresponding singular vectors, and block Lanczos with warm start (BLWS). The current version is preliminary. The details will be enriched soon.

Multiplicative backward stability results are presented for two algorithms which compute the singular value decomposition of dense matrices. These algorithms are the classical onesided Jacobi algorithm, with a stringent stopping criterion, and an algorithm which uses one-sided Jacobi to compute high accurate singular value decompositions of matrices given as rank-revealing factorizations. When ...

mobile ad-hoc networks (manets) by contrast of other networks have more vulnerability because of having nature properties such as dynamic topology and no infrastructure. therefore, a considerable challenge for these networks, is a method expansion that to be able to specify anomalies with high accuracy at network dynamic topology alternation. in this paper, two methods proposed for dynamic anom...

Lanczos bidiagonalization is a competitive method for computing a partial singular value decomposition of a large sparse matrix, that is, when only a subset of the singular values and corresponding singular vectors are required. However, a straightforward implementation of the algorithm has the problem of loss of orthogonality between computed Lanczos vectors, and some reorthogonalization techn...

We present deviation inequalities of random operators of the form 1 N ∑N i=1 Xi ⊗ Xi from the average operator E(X ⊗ X), where Xi are independent random vectors distributed as X, which is a random vector in R or in `2. We use these inequalities to estimate the singular values of random matrices with independent rows (without assuming that the entries are independent).

We compute the singular value decomposition of the radial distribution function g(r) for hard sphere, and square well solutions. We find that g(r) decomposes into a small set of basis vectors allowing for an extremely accurate representation at all interpolated densities and potential strengths. In addition, we find that the coefficient vectors describing the magnitude of each basis vector are ...

We introduce the T -restricted weighted generalized inverse of a singular matrix A with respect to a positive semidefinite matrix T , which defines a seminorm for the space. The new approach proposed is that since T is positive semidefinite, the minimal seminorm solution is considered for all vectors perpendicular to the kernel of T .

We introduce the T -restricted weighted generalized inverse of a singular matrix A with respect to a positive semidefinite matrix T , which defines a seminorm for the space. The new approach proposed is that since T is positive semidefinite, the minimal seminorm solution is considered for all vectors perpendicular to the kernel of T .