A Highly Efficient and Accurate Finite Iterative Method for Solving Linear Two-Dimensional Fredholm Fuzzy Integral Equations of the Second Kind Using Triangular Functions

This work introduces a computational method for solving the linear two-dimensional fuzzy Fredholm integral equation of the second form (2D-FFIE-2) based on triangular basis functions. We have used the parametric form of fuzzy functions and transformed a 2D-FFIE-2 with three variables in crisp case to a linear Fredholm integral equation of the second kind. First, a method based on the use of two m-sets of orthogonal functions of triangular form is implemented on the integral equation under study to be changed to coupled algebraic equation system. In order to solve these two schemes, a finite iterative algorithm is then applied to evaluate the coefficients that provided the approximate solution of the integral problems. Three examples are given to clarify the efficiency and accuracy of the method. The obtained numerical results are compared with other direct and exact solutions.

A Modified Algorithm for the Computation of the Covariance Matrix Implied by a Structural Recursive Model with Latent Variables Using the Finite Iterative Method

Structural Equation Modeling (SEM) is a statistical technique that assesses a hypothesized causal model byshowing whether or not, it fits the available data. One of the major steps in SEM is the computation of the covariance matrix implied by the specified model. This matrix is crucial in estimating the parameters, testing the validity of the model and, make useful interpretations. In the present paper, two methods used for this purpose are presented: the J¨oreskog’s formula and the finite iterative method. These methods are characterized by the manner of the computation and based on some apriori assumptions. To make the computation more simplistic and the assumptions less restrictive, a new algorithm for the computation of the implied covariance matrix is introduced. It consists of a modification of the finite iterative method. An illustrative example of the proposed method is presented. Furthermore, theoretical and numerical comparisons between the exposed methods with the proposed algorithm are discussed and illustrated