We show that preconditioners constructed by random sampling can perform well without meeting the standard requirements of iterative methods. When applied to graph Laplacians, this leads to ultrasparsifiers that in expectation behave as the nearly-optimal ones given by [Kolla-Makarychev-Saberi-Teng STOC‘10]. Combining this with the recursive preconditioning framework by [Spielman-Teng STOC‘04] a...

Abstract ScaLAPACK contains a pair of routines for solving systems which are narrow banded and diagonally dominant by rows. Mathematically, the algorithm is block cyclic reduction. The ScaLAPACK implementation can be improved using incomplete, rather than complete block cyclic reduction. If the matrix is strictly dominant by rows, then the truncation error can be bounded directly in terms of th...

Recently, Laplacian matrices of graphs are studied as density matrices in quantum mechanics. We continue this study and give conditions for separability of generalized Laplacian matrices of weighted graphs with unit trace. In particular, we show that the Peres-Horodecki positive partial transpose separability condition is necessary and sufficient for separability in C2 ⊗ C. In addition, we pres...

Inter-cell cochannel interference (ICCI) is an inherent problem in all cellular systems due the necessity to reuse the same frequencies after a certain reuse distance. In GSM, the fact that the number of nearby cochannel interferers is relatively small leads to a high probability of a dominant interferer (DI). Hence, suppression of DI alone provides substantial capacity improvement for GSM. The...

Interconnected networks describe the dynamics of important systems in a wide range such as biological systems and electrical power grids. Some important features of these systems were successfully studied and understood through simplified model of linear interconnection of linear subsystems, where provably global properties, e.g. global convergence to a specific state, usually hold true. Howeve...

In this paper, we propose a fast distributed solver for linear equations given by symmetric diagonally dominant M-Matrices. Our approach is based on a distributed implementation of the parallel solver of Spielman and Peng by considering a specific approximated inverse chain which can be computed efficiently in a distributed fashion. Representing the system of equations by a graph G, the propose...

A robust Nyquist array analysis for MIMO systems is proposed based on uncertainty descriptions obtained from system identi'cation. Two types of statistical-based uncertainty error bounds for the frequency response are obtained: element bounds and column bounds. Gershgorin’s theorem and the concepts of diagonal dominance and Gershgorin bands are extended to include model uncertainty. Robust stab...

The solution of a general block tridiagonal linear system by a cyclic odd-even reduction algorithm is considered. Under conditions of diagonal dominance, norms describing the off-diagonal blocks relative to the diagonal blocks decrease quadratically with each reduction. This allows early termination of the reduction when an approximate solution is desired. The algorithm is well-suited for paral...

This paper provides a solution to the curse of dimensionality problem in the pairwise scoring techniques that are commonly used in bioinformatics and biometrics applications. It has been recently discovered that stacking the pairwise comparison scores between an unknown patterns and a set of known patterns can result in feature vectors with nice discriminative properties for classification. How...