Two fast algorithms for numerically computing an interval matrix containing the solvent of the quadratic matrix equation AX2+BX+C = 0 with square matrices A, B, C and X are proposed. These algorithms require only cubic complexity, verify the uniqueness of the contained solvent, and do not involve iterative process. Let X̃ be a numerical approximation to the solvent. The first and second algorith...

A class of hyperbolic distributed parameter time-varying system on the interval [0,∞) is considered. The corresponding linear-quadratic (LQ) optimal control problem is studied by using the infinite-dimensional state-space formulation and the well-known Riccati equation approach.

<abstract><p>Consider the problem of finding maximal nonpositive solvent $ \varPhi quadratic matrix equation (QME) X^2 + BX C = 0 with B being a nonsingular M $-matrix and an such that B^{-1}C\ge $. Such QME arises from overdamped vibrating system. Recently, under condition - I is $-matrix, Yu et al. (<italic>Appl. Math. Comput.</italic>, 218 (2011): 3303–3310) proved \r...

We study the solvability of a quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions. AMS Mathematics Subject Classification : 45G10, 45M99, 47H09.

a matrix $pintextmd{c}^{ntimes n}$ is called a generalized reflection matrix if $p^{h}=p$ and $p^{2}=i$‎. ‎an $ntimes n$‎ ‎complex matrix $a$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $p$ if $a=pap$ ($a=-pap$)‎. ‎in this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $axb=c$ and $dxe=f$ over reflexiv...