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...

The algorithm of construction of solutions of the unilateral quadratic matrix equation in case of complex eigenvalues of the corresponding matrix pencil is offered. As application, the problem of updating parameters of model by experimentally estimation of eigenvalues of this system is considered. Efficiency of the offered procedure of updating is shown on the example of system with two degree ...

New algorithms for solving algebraic Riccati equations (ARE) which arise in fluid queues models are introduced. They are based on reducing the ARE to a unilateral quadratic matrix equation of the kind AX2 + BX + C = 0 and on applying the Cayley transform in order to arrive at a suitable spectral splitting of the associated matrix polynomial. A shifting technique for removing unwanted eigenvalue...

None of the usual floating point numerical techniques available for solving the quadratic matrix equation AX +BX +C = 0 with square matrices A,B, C and X, can provide an exact solution; they can just obtain approximations to an exact solution. We use interval arithmetic to compute an interval matrix which contains an exact solution to this quadratic matrix equation, where we aim at obtaining na...

None of the usual floating point numerical techniques available for solving the quadratic matrix equation AX +BX +C = 0 with square matrices A,B, C and X, can provide an exact solution; they can just obtain approximations to an exact solution. We use interval arithmetic to compute an interval matrix which contains an exact solution to this quadratic matrix equation, where we aim at obtaining na...

A new boundary condition is introduced to calculate the effective impedance matrix of semi-infinite periodic structures such as photonic crystals and metamaterials, which leads to a reduction of the solution space. The obtained effective impedance matrix allows one to relate a matrix to a PC, which includes all of its properties in terms of reflection from its interface. For one-dimensional pho...

It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...

in this article, we characterize the involutiveness of the linear combination of the forma1a1 +a2a2 when a1, a2 are nonzero complex numbers, a1 is a quadratic or tripotent matrix,and a2 is arbitrary, under certain properties imposed on a1 and a2.