It is well known that the trapezoidal rule converges geometrically when applied to analytic functions on periodic intervals or the real line. The mathematics and history of this phenomenon are reviewed and it is shown that far from being a curiosity, it is linked with computational methods all across scientific computing, including algorithms related to inverse Laplace transforms, special funct...

Many authors analyzed triangular and trapezoidal approximation of fuzzy numbers. But, to best of our knowledge, there is no method for symmetric trapezoidal fuzzy number approximation of fuzzy numbers. So, in this paper, we try to convert any fuzzy number into symmetric trapezoidal fuzzy number by using metric distance. This approximation helps us to avoid the computational complexity in the pr...

Class Sm variable transformations with integer m, for accurate numerical computation of finite-range integrals via the trapezoidal rule, were introduced and studied by the author. A representative of this class is the sinm -transformation. In a recent work of the author, this class was extended to arbitrary noninteger values of m, and it was shown that exceptionally high accuracies are achieved...

In the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(P,Q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}A_{l}XB_{l}+overset{v} ‎{underset{s=1}{sum}}C_{s}widetilde{X}D_{s}=F$‎. ‎By this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎When the‎ ‎matrix equation is consistent over...

It is generally agreed that of all quadrature formulae, the trapezoidal rule, while being the simplest, is also the least accurate. There is, however, a rather general class of integrals for which the trapezoidal rule can be shown to be a highly accurate means of obtaining numerical values. Specifically, if the integrand is a periodic, even function with all derivatives continuous, then the int...

Defuzzification is the process of converting a fuzzy quantity to precise quantity, just as fuzzification is the conversion of a precise quantity to a fuzzy quantity. Various types of defuzzification methods, are available for conversion of fuzzy to non-fuzzy. In this paper, defuzzification functions in intuitionistic fuzzy environment such as triangular, trapezoidal, L-trapezoidal, R-trapezoida...

There is a growing interest in building probabilistic models with high order potentials (HOPs), or interactions, among discrete variables. Message passing inference in such models generally takes time exponential in the size of the interaction, but in some cases maximum a posteriori (MAP) inference can be carried out efficiently. We build upon such results, introducing two new classes, includin...

trapezoidal channels are frequently used in irrigation networks and other free surface water conveyance systems. the computation of the critical flow depth is one of the primary importance in the design process. it is usually determined by using design charts of iteration techniques. however, researchers have recently proposed formulas that directly provide approximate solutions. this paper pre...

In this paper, we propose and analyze a new predictor-corrector method for solving a nonlinear system of equations using the weight combination of mid-point, Trapezoidal and quadrature formulas. A new algorithm based on this method has been presented. The proposed method has been tested on a series of examples published in the literature and shows good results. Comparison with other similar met...

The basic transportation problem was originally developed by Hitchcock. In the literature several methods are proposed for solving Fuzzy transportation problem. In this paper, we propose a new algorithm called Fuzzy Russell’s method for the initial basic feasible solution to a Fuzzy transportation problem. To examine the proposed method a numerical example is solved. Fuzzy numbers may be normal...