The Stable Solutions of Quadratic Matrix Equations

Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets

This paper introduces the emph{interval unilateral quadratic matrix equation}, $IUQe$ and attempts to find various analytical results on its AE-solution sets in which $A,B$ and $CCC$ are known real interval matrices, while $X$ is an unknown matrix. These results are derived from a generalization of some results of Shary. We also give sufficient conditions for non-emptiness of some quasi-solutio...

On the Solutions of Quadratic Diophantine Equations

We determine a finite set of representatives of the set of local solutions in a maximal lattice modulo the stabilizer of the lattice in question for a quadratic Diophantine equation. Our study is based on the works of Shimura on quadratic forms, especially [AQC] and [IQD]. Indeed, as an application of the result, we present a criterion (in both global and local cases) of the maximality of the l...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

A stable iteration to the matrix inversion

The matrix inversion plays a signifcant role in engineering and sciences. Any nonsingular square matrix has a unique inverse which can readily be evaluated via numerical techniques such as direct methods, decomposition scheme, iterative methods, etc. In this research article, first of all an algorithm which has fourth order rate of convergency with conditional stability will be proposed. ...

Fast verification of solutions of matrix equations

In this paper, we are concerned with a matrix equation Ax = b where A is an n× n real matrix and x and b are n-vectors. Assume that an approximate solution e x is given together with an approximate LU decomposition. We will present fast algorithms for proving nonsingularity of A and for calculating rigorous error bounds for ‖A−1b − e x‖∞. The emphasis is on rigour of the bounds. The purpose of ...