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 .

Many algebraic preconditioners rely on incomplete factorization, where nonzero entries are dropped, based on some rule, during the factorization process. In a series of papers by Bollhöfer and Saad [2, 3, 4] it was shown that robust rules for both dropping and pivoting can be obtained from information about the inverses of the submatrices that are consecutively constructed. In particular, monit...

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 .

Globalization, and the resultant movement of animals beyond their native range, creates challenges for biosecurity agencies. Limited records of unintentional introductions inhibit our understanding of the trade pathways, transport vectors and mechanisms through which hitchhiker organisms are spread as stowaways. Here, we adopt a phylogeographic approach to determine the source and human-mediate...