The current paper contributes a novel framework for solving a class of linear matrix differential equations. To do so, the operational matrix of the derivative based on the shifted Bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. An error estimation of presented method is provided. Numerical experiments are...

This paper discusses an algorithm and its implementation for solving a system of linear equations on a distributed system. The algorithm used is The Cramer's rule for solving a large number of linear equations simultaneously. Hence, a pivotal part of this algorithm is solving a determinant of a square matrix in a distributed manner. This topic of determinant solving is discussed in detail, foll...

fuzzy liner systems of equations, play a major role in several applications in various area such as engineering, physics and economics. in this paper, we investigate the existence of a minimal solution of inconsistent fuzzy matrix equation. also some numerical examples are considered.

this paper analyzes a linear system of equations when the righthandside is a fuzzy vector and the coefficient matrix is a crisp m-matrix. thefuzzy linear system (fls) is converted to the equivalent crisp system withcoefficient matrix of dimension 2n × 2n. however, solving this crisp system isdifficult for large n because of dimensionality problems . it is shown that thisdifficulty may be avoide...

where T(6), U(6), V(6) and W(6) are polynomial matrices in the indeterminate 6, which for recurrent equations can have the meaning of the one-step forward-shift operator. He showed that under the polynomial transformations on (1.1), (1.2) that he called strict system equivalence, if T(6) is square, detT(6) ^ 0 (and has a degree equal to the dimension of T(6)) and the input-output transfer matri...

We propose a hybrid algorithm for solving the NP-hard absolute value equation (AVE): Ax−|x| = b, where A is an n×n square matrix. The algorithm makes no assumptions on the AVE other than solvability and consists of solving iteratively a linear system of equations followed by a linear program. The algorithm was tested on 100 consecutively generated random solvable instances of the AVE with n =50...

We consider the solution of the ?-Sylvester equation AX±X?B? = C, for ? = T,H and A,B,∈ Cm×n, and some related linear matrix equations (AXB? ± X? = C, AXB? ± CX?D? = E, AX ± X?A? = C, AX ± Y B = C, AXB ± CY D = E, AXA? ± BY B? = C and AXB ± (AXB)? = C). Solvability conditions and stable numerical methods are considered, in terms of the (generalized and periodic) Schur, QR and (generalized) sing...

This paper addresses the QR decomposition and UD factorization based square-root algorithms of the recursive least-squares (RLS) Wiener fixed-point smoother and filter. In the RLS Wiener estimators, the Riccati-type difference equations for the auto-variance function of the filtering estimate are included. Hence, by the roundoff errors, in the case of the small value of the observation noise va...

Here we present a new approach to calculating the square root of a quadratic matrix. Actually, the purpose of this article is to show how the Cayley-Hamilton theorem may be used to determine an explicit formula for all the square roots of $2times 2$ matrices.

In this paper, the numerical technique based on hybrid Bernoulli and Block-Pulse functions has been developed to approximate the solution of system of linear Volterra integral equations. System of Volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. These functions are formed by the hybridi...