in this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. also necessary and sufficient conditions for existenceof solution are given. some numerical examples illustrate the efficiencyof the method.

We show that Levinson's basic principle for the solution of normal equations which are of Toeplitz form may he extended to the case where these equations do not possess this specific symmetry. The use of Levinson's principle allows us to obtain a compact ( 2 x 2 ) form to express a system of equations of arbitrary order. This compact form is the key expression in the development of recursive al...

Let U be a real n x n matrix whose entries uij are random variables, and let A and B be fixed n x n real symmetric matrices. Statisticians (e.g., see [OU]) have been interested in the distribution of the eigenvalues d l , . . . , O n of the matrix AUBUt, where denotes transpose. Of particular interest are the quantities tr((AU = C 0; for k = 1,2,. . . , since these determine the eigenvalues. Mo...

where y is the n× 1 response vector; X is an n× p model matrix representing the predictors; and β is a p × 1 vector of coefficients to estimate. For mathematical simplicity, it is typical to set the first predictor as the intercept β0 so that the first column of X is the n×1 vector of ones. The intercept acts as a sink for the mean effect of included predictors, so one could remove the intercep...

and Applied Analysis 3 As is well known, compared with linear matrix inequalities (LMIs) result, algebraic result is more conservative, and criteria in terms of LMI can be easily checked by using the powerful Matlab LMI toolbox. This motivates us to investigate the problems of the uniformly ultimate boundedness and the existence of an attractor for switchedCGNN in this paper. The illustrative e...

The performance of a polarizing beam splitter based on the one-dimensional photonic crystals (1D-PCs), is theoretically investigated. The polarizing beam splitter consists of a symmetric stack of the low-index quarter-wave plates and the high-index half-wave plates with a central defect layer of air. The linear transmission properties of the polarizing beam splitter are numerically simulat...

Abstract In this paper, which is a follow-up to Borobia et al. (Mediterr J Math, 18:40, 2021), we provide necessary and sufficient condition for the matrix equation $$X^\top AX=B$$ X ⊤ A = B be co...

‎The global FOM and GMRES algorithms are among the effective‎ ‎methods to solve Sylvester matrix equations‎. ‎In this paper‎, ‎we‎ ‎study these algorithms in the case that the coefficient matrices‎ ‎are real symmetric (real symmetric positive definite) and extract‎ ‎two CG-type algorithms for solving generalized Sylvester matrix‎ ‎equations‎. ‎The proposed methods are iterative projection metho...

‎the global fom and gmres algorithms are among the effective‎ ‎methods to solve sylvester matrix equations‎. ‎in this paper‎, ‎we‎ ‎study these algorithms in the case that the coefficient matrices‎ ‎are real symmetric (real symmetric positive definite) and extract‎ ‎two cg-type algorithms for solving generalized sylvester matrix‎ ‎equations‎. ‎the proposed methods are iterative projection metho...