The matrix inequality M ⩾ B∗MB

On the modified iterative methods for $M$-matrix linear systems

This paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. Recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the Accelerated Overrelaxation (AOR) method. In this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditio...

SOLVING FUZZY LINEAR SYSTEMS BY USING THE SCHUR COMPLEMENT WHEN COEFFICIENT MATRIX IS AN M-MATRIX

This paper analyzes a linear system of equations when the righthandside is a fuzzy vector and the coefficient matrix is a crisp M-matrix. Thefuzzy linear system (FLS) is converted to the equivalent crisp system withcoefficient matrix of dimension 2n × 2n. However, solving this crisp system isdifficult for large n because of dimensionality problems . It is shown that thisdifficulty may be avoide...

The matrix arithmetic-geometric mean inequality revisited

Matrix sparsification via the Khintchine inequality

Given a matrix A ∈ Rn×n, we present a simple, element-wise sparsification algorithm that zeroes out all sufficiently small elements of A, keeps all sufficiently large elements of A, and retains some of the remaining elements with probabilities proportional to the square of their magnitudes. We analyze the approximation accuracy of the proposed algorithm using a powerful inequality bounding the ...

A Linear Matrix Inequality Approach

This paper addresses the problem of designing stabilizing controllers that minimize the 7 l ~ norm of a certain closed-loop transfer function while maintaining the C1 norm of a different transfer function below a prespecified level. This problem arises in the context of rejecting both stochastic as well as bounded persistent disturbances. Alternatively, in a robust control framework it can be t...