Interval-constrained matrix balancing

Energy-Constrained Balancing

This paper defines and analyzes a fundamental energy-constrained balancing problem, in which elements need to be balanced across resources in order to minimize the increasing convex cost function associated with the load at each resource. However, the balancing operation needs to satisfy average and instantaneous constraints on the energy associated with checking the current load of the many re...

Balancing Regular Matrix Pencils

In this paper we present a new diagonal balancing technique for regular matrix pencils λB − A, which aims at reducing the sensitivity of the corresponding generalized eigenvalues. It is inspired from the balancing technique of a square matrix A and has a comparable complexity. Upon convergence, the diagonally scaled pencil has row and column norms that are balanced in a precise sense. We also s...

A Space-Constrained Interval Selection

In this paper we consider the interval selection problem, namely, finding a maximum cardinality subset of disjoint intervals from a given collection of intervals on the real line. A celebrated algorithm of Gavril [17] that picks the intervals greedily in increasing order of their right endpoint yields an optimal solution in the classic setting where the complete set of intervals is known to the...

Gauss elimination algorithm for interval matrix

‎A matrix LSQR algorithm for solving constrained linear operator equations

In this work‎, ‎an iterative method based on a matrix form of LSQR algorithm is constructed for solving the linear operator equation $mathcal{A}(X)=B$‎ ‎and the minimum Frobenius norm residual problem $||mathcal{A}(X)-B||_F$‎ ‎where $Xin mathcal{S}:={Xin textsf{R}^{ntimes n}~|~X=mathcal{G}(X)}$‎, ‎$mathcal{F}$ is the linear operator from $textsf{R}^{ntimes n}$ onto $textsf{R}^{rtimes s}$‎, ‎$ma...