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In this paper, we investigate the interval coupled Sylvester matrix equations which include the well-known (generalized) Sylvester and Lyapunov matrix equations in both real and interval forms. Assuming that certain matrices are simultaneously diagonalizable, we present a fast and efficient approach for enclosing the solution set of the interval coupled Sylvester matrix equations. Our approach, which is a modification of the Krawczyk operator, enables us to reduce the computational complexity considerably. Some numerical tests are given to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of Moore-Penrose inverse of a rectangular interval matrix based on a modified interval arithmetic. We determine the Moore-Penrose inverse in such a way that it satisfies all the four criteria similar to the real case. Also, we use the Moore-Penrose inverse for solving rectangular interval linear systems, algebraically. [ABSTRACT FROM AUTHOR]

In this paper we present the LU decomposition of a generalized interval matrix A under a modified interval arithmetic. This modified interval arithmetic is defined on generalized intervals and possesses group properties with respect to the addition and multiplication operations. These properties cause that the two computed generalized interval matrices L and U from the LU decomposition satisfy A = LU, with equality in modified interval arithmetic instead of the weaker inclusion in the classical interval arithmetic. Some applications of the new technique for solving interval linear systems are given and effectiveness of the new approach is investigated along some numerical tests. [ABSTRACT FROM AUTHOR]

In this paper, we describe and analyze an efficient method to find the roots of a general one variable function f: R ? R. The proposed method is based on partitioning an interval (that probably contains root(s) of f) into subintervals. From this point of view, we name this method a finite element approach for root finding. Also the convergence analysis of the presented method is presented. The new approach can be generalized to estimate the roots of the multivariable functions in higher dimensions. Also it is capable to find all of the roots of the function on a determined interval. Finally, numerical examples are given to illustrate the effectiveness of the new method. [ABSTRACT FROM AUTHOR]

In this paper, parametric Sylvester matrix equations whose elements are linear functions of interval parameters are considered. In contrast to deterministic problems, when a system of equations is derived from a stochastic model, its coefficients may depend on some parameters and so the parameterized system of equations appears. This work considers the parameterized Sylvester matrix equations and tries to propose some methods containing a direct method and two iterative methods to obtain outer estimations of the solution set. [ABSTRACT FROM AUTHOR]

In this work, we study the parametric Sylvester matrix equation A (p) X + X B (p) = C (p) whose elements are linear functions of uncertain parameters varying within some intervals. We first explore some properties of its solution set and then present some sufficient conditions for boundedness of the solution set. The main work is developing a modified variant of the parametric Krawczyk operator which reduces the computational complexity of enclosing the solution set significantly, compared to the parametric Krawczyk operator on the Kronecker product form. Some numerical experiments are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Generalized intervals (intervals whose bounds are not constrained to be increasingly ordered) extend classical intervals and present algebraic completion of conventional interval arithmetic, allowing efficient solution for interval linear systems. In this paper, we use the Cholesky decomposition of a symmetric generalized interval matrix A introduced by Zhao et al. (A generalized Cholesky decomposition for interval matrix, Adv. Mat. Res. 479 (2012) 825{828), to construct the algebraic solution of the triangular interval linear system of equations. Also we utilize this decomposition to find inner and outer estimations of the generalized solution set of the symmetric interval linear systems. Finally some numerical experiments and an application in economic are given to show the efficiency of the presented technique. [ABSTRACT FROM AUTHOR]

In this paper, the parametric matrix equation A( p) X = B( p) whose elements are linear functions of uncertain parameters varying within intervals are considered. In this matrix equation A( p) and B( p) are known m-by- m and m-by- n matrices respectively, and X is the m-by- n unknown matrix. We discuss the so-called AE-solution sets for such systems and give some analytical characterizations for the AE-solution sets and a sufficient condition under which these solution sets are bounded. We then propose a modification of Krawczyk operator for parametric systems which causes reduction of the computational complexity of obtaining an outer estimation for the parametric united solution set, considerably. Then we give a generalization of the Bauer-Skeel and the Hansen-Bliek-Rohn bounds for enclosing the parametric united solution set which also enables us to reduce the computational complexity, significantly. Also some numerical approaches based on Gaussian elimination and Gauss-Seidel methods to find outer estimations for the parametric united solution set are given. Finally, some numerical experiments are given to illustrate the performance of the proposed methods. [ABSTRACT FROM AUTHOR]