Abstract: In this paper, fully fuzzy linear systems in the form ° ° % A X = b ⊗ (FFLS) will be discussed, where ° n n A × is a fuzzy matrix, x and b are (n×1) fuzzy vector. Transforming fully fuzzy linear system in to two crisp linear systems and using the Jacobi iterative and Adomian Decomposition Methods (ADM) a FFLS will be solved.We will show that to find a solution for a (FFLS) our method ...

We announce three results in the theory of Jacobi matrices and Schrödinger operators. First, we give necessary and sufficient conditions for a measure to be the spectral measure of a Schrödinger operator − d dx +V (x) on L2(0,∞) with V ∈ L2(0,∞) and u(0) = 0 boundary condition. Second, we give necessary and sufficient conditions on the Jacobi parameters for the associated orthogonal polynomials...

Jacobi Matrices (real symmetric tridiagonal matrices) have a wide range of applications in physics and engineering, and are closely and non-trivially linked with many other mathematical objects, such as orthogonal polynomial, one dimensional Schrödinger operators and the Sturm-Liouville problem. In the past couple of decades, constructing Jacobi matrices from different types of data was studied...

A variableband relaxation algorithm for solving large linear systems is developed as an alternative to Gaues-Jacobi relaxation. This algorithm seeks to improve the reliability of Gauss-Jacobi relaxation by extracting a variable-sized band from the matrix and solving that band directly. This leads to a relaxation algorithm with provably better convergence p rop erties. Furthermore, this algorith...

This paper describes the robust output feedback ∞ H fuzzy control design for a class of nonlinear stochastic systems. The system dynamic is modelled by type ô It − stochastic differential equations. For general nonlinear stochastic systems, the ∞ H ontrol can be obtained by solving a second-order nonlinear Hamilton-Jacobi inequality. In general, it is difficult to solve the second-order nonline...

We introduce in this paper a method to calcúlate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G. Mantica to calcúlate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures. We apply this method to approximate the Hessenberg matrix associated wit...

Jacobi-based algorithms have attracted attention as they have a high degree of potential parallelism and may be more accurate than QR-based algorithms. In this paper we discuss how to design efficient Jacobi-like algorithms for eigenvalue decomposition of a real normal matrix. We introduce a block Jacobi-like method. This method uses only real arithmetic and orthogonal similarity transformation...

In this paper, we develop a Jacobi-Gauss-Lobatto collocation method for solving the nonlinear fractional Langevin equation with three-point boundary conditions. The fractional derivative is described in the Caputo sense. The shifted Jacobi-Gauss-Lobatto points are used as collocation nodes. The main characteristic behind the Jacobi-Gauss-Lobatto collocation approach is that it reduces such a pr...

The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials. Expansions in terms of orthogonal polynomials are very common in many applications. While the connection problem may be solved by directly computing the change–of–basis matrix, ...

We report on a parallel implementation of the Jacobi–Davidson (JD) to compute a few eigenpairs of a large real symmetric generalized matrix eigenvalue problem