lsmr (least squares minimal residual) is an iterative method for the solution of the linear system of equations and leastsquares problems. this paper presents a block version of the lsmr algorithm for solving linear systems with multiple right-hand sides. the new algorithm is based on the block bidiagonalization and derived by minimizing the frobenius norm of the resid ual matrix of normal equa...

In this paper, we consider the system of linear equations Ax̃ = b̃, where A ∈ Rn×n is a crisp H-matrix and b̃ is a fuzzy n-vector. We then investigate the existence and uniqueness of a fuzzy solution to this system. The results can also be used for the class of M-matrices and strictly diagonally dominant matrices. Finally, some numerical examples are given to illustrate the presented theoretical r...

As can be seen from the definition of extended operations on fuzzy numbers, subtraction and division of fuzzy numbers are not the inverse operations to addition and multiplication, respectively. Hence for solving equations or system of equations, we must use methods without using inverse operators. In this paper, we propose a novel method to find the nonzero solutions of fully fuzzy linear syst...

we present a model and propose an approach to compute an approximate solution of fully fuzzy linear system $(ffls)$ of equations in which all the components of the coefficient matrix are either nonnegative or nonpositive. first, in discussing an $ffls$ with a nonnegative coefficient matrix, we consider an equivalent $ffls$ by using an appropriate permutation to simplify fuzzy multiplications. t...

in this paper the solution of a second order linear dierential equations with intu-itionistic fuzzy boundary value is described. it is discussed for two dierent cases: coecientis positive crisp number and coecient is negative crisp number. here fuzzy numbers aretaken as generalized trapezoidal intutionistic fuzzy numbers (gtrifns). further a numericalexample is illustrated.

In this paper, a matrix formulation of fuzzy rule based systems is introduced. A gradient descent training algorithm for the determination of the unknown parameters can also be expressed in a matrix form for various adaptive fuzzy networks. When converting a rule-based system to the proposed matrix formulation, only three sets of linear/nonlinear equations are required instead of set of rules a...

This paper presents a Takagi-Sugeno fuzzy model-based controller which stabilizes the attitude of spacecraft with a partially-filled fuel tank. First, the nonlinear equations of motion of spacecraft containing a liquid fuel store is presented briefly. Then, the fuzzy modeling and the parallel distributed compensation control technique are applied. The proposed fuzzy controller is a nonlinear co...

in this paper we consider the problem of delay-dependent robusth1 control for uncertain fuzzy systems with time-varying delay. the takagi–sugeno (t–s) fuzzy model is used to describe such systems. time-delay isassumed to have lower and upper bounds. based on the lyapunov-krasovskiifunctional method, a sufficient condition for the existence of a robust $h_{infty}$controller is obtained. the fuzz...