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...

Our weakly random additive preconditioners facilitate the solution of linear systems of equations and other fundamental matrix computations. Compared to the popular SVD-based multiplicative preconditioners, these preconditioners are generated more readily and for a much wider class of input matrices. Furthermore they better preserve matrix structure and sparseness and have a wider range of appl...

With a high probablilty our randomized augmentation of a matrix eliminates its rank deficiency and ill conditioning. Our techniques avoid various drawbacks of the customary algorithms based on pivoting and orthogonalization, e.g., we readily preserve matrix structure and sparseness. Furthermore our randomized augmentation is expected to precondition quite a general class of ill conditioned inpu...

The equilibrium state probabilities for queues with batch Markovian arrival processes are determined in form of matrix expressions, in which the central item to be computed is the so called fundamental-period-matrix G . G appears as the solution of the non-linear matrix equation G = AνG ν Σ , or as the infinite sum over matrices Gν , which in turn are functions of the matrices Aν as has been sh...

With a high probablilty our randomized augmentation of a matrix eliminates its rank deficiency and ill conditioning. Our techniques avoid various drawbacks of the customary algorithms based on pivoting and orthogonalization, e.g., we readily preserve matrix structure and sparseness. Furthermore our randomized augmentation is expected to precondition quite a general class of ill conditioned inpu...

In this study, a method is proposed to determine the fundamental period of layered soil profiles. A model considering the layered soil as shear type structure is used. At first, the soil profile is divided into substructures. Then, the stiffness matrices of the substructures considered as the equivalent shear structures are assembled according to the Finite Element Method. Thereinafter, the sti...

In this paper we propose and implement numerical methods to detect exponential dichotomy on the real line. Our algorihtms are based on the singular value decomposition and the QR factorization of a fundamental matrix solution. The theoretical justification for our methods was laid down in the companion paper [15].

The Magnus series is an infinite series which arises in the study of linear ordinary differential equations. If the series converges, then the matrix exponential of the sum equals the fundamental solution of the differential equation. The question considered in this paper is: When does the series converge? The main result establishes a necessary condition for convergence, which improves on seve...

In this work, we introduce and analyze two new techniques for obtaining the Q factor in the QR factorization of some (or all) columns of a fundamental solution matrix Y of a linear diierential system. These techniques are based on elementary Householder and Givens transformations. We implement and compare these new techniques with existing approaches on some examples.