This study proposes an algorithm capable of working in parallel for solving large and sparse linear equations under given right hand side (RHS) ranges. A comparative study to the direct linear programming method is reported theoretically, computationally and discussed. Moreover, the approach can be adapted for the system under domain decompositions structure leading to a better efficiency exper...

The spectrum of the eigenvalues, the conditioning, and other related properties of circulant-like matrices used to build up block preconditioners for the nonsymmetric algebraic linear equations of time-step integrators for linear boundary value problems are analyzed. Moreover, results concerning the entries of a class of Toeplitz matrices related to the latter are proposed. Generalizations of i...

We present computational results using CORAL, a parallel, three-dimensional, nonlinear magnetostatic code based on a volume integral equation formulation. A key feature of CORAL is the ability to solve, in parallel, the large, dense systems of linear equations that are inherent in the use of integral equation methods. Using the Chameleon and PSLES libraries ensures portability and access to the...

A sparse linear system constitutes a valid model for a broad range of physical systems, such as electric power networks, industrial processes, control systems or traffic models. The physical magnitudes in those systems may be directly measured by means of sensor networks that, in conjunction with data obtained from contextual and boundary constraints, allow the estimation of the state of the sy...

Algebraic geometry plays an important role in the theory of linear systems for (at least) three reasons. First, the Laplace transform turns expressions about linear differential systems into expressions involving rational functions. In addition, many of the transformations studied in linear systems theory, like changes of coordinates or feedback, turn out to be the action of algebraic groups on...

Likelihood ratio criteria are developed for hypotheses concerning multivariate regression matrices when reduced rank is assumed or equivalently hypotheses concerning linear restrictions on regression matrices. In an econometric simultaneous equation model a single restriction may be called a ”structural equation.” A model of reduced rank in statistics is often termed a ”linear functional relati...

Exploiting sparsity has been a key issue in solving large-scale optimization problems. The most time-consuming part of primal-dual interior-point methods for linear programs, secondorder cone programs, and semidefinite programs is solving the Schur complement equation at each iteration, usually by the Cholesky factorization. The computational efficiency is greatly affected by the sparsity of th...

We propose novel algorithms to calculate the inverses of ill-conditioned matrices, which have broad engineering applications. The vector-form of the conjugate gradient method (CGM) is recast into a matrix-form, which is named as the matrix conjugate gradient method (MCGM). The MCGM is better than the CGM for finding the inverses of matrices. To treat the problems of inverting illconditioned mat...

This paper offers new necessary and sufficient conditions for delaydependent asymptotic stability of the linear continuous large scale time delay systems. The obtained conditions of stability are expressed by nonlinear system of matrix equations and the Lyapunov matrix equation for an ordinary linear continuous system without delay.