A. Rivaz
Department of Mathematics and Computer Science, Shahid Bahonar University of Kerman, P.O.Box 761691, Kerman, Iran
[ 1 ] - Convergence analysis of the global FOM and GMRES methods for solving matrix equations $AXB=C$ with SPD coefficients
In this paper, we study convergence behavior of the global FOM (Gl-FOM) and global GMRES (Gl-GMRES) methods for solving the matrix equation $AXB=C$ where $A$ and $B$ are symmetric positive definite (SPD). We present some new theoretical results of these methods such as computable exact expressions and upper bounds for the norm of the error and residual. In particular, the obtained upper...
[ 2 ] - 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...
[ 3 ] - Analytical and Verified Numerical Results Concerning Interval Continuous-time Algebraic Riccati Equations
This paper focuses on studying the interval continuous-time algebraic Riccati equation A∗X + XA + Q − XGX = 0, both from the theoretical aspects and the computational ones. In theoretical parts, we show that Shary’s results for interval linear systems can only be partially generalized to this interval Riccati matrix equation. We then derive an efficient technique for enclosing the united stable...
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