A Numerical Approach for Computing Standard Errors of Linear Equating

Asymptotic Standard Errors of IRT Equating Coefficients Using Moments

The asymptotic standard errors of the IRT equating coefficients given by the mean/sigma, mean/mean and mean/geometric mean methods are derived when the two-parameter logistic model holds and item parameters are obtained by the marginal maximum likelihood estimation. The case of two nonequivalent examinee-groups and the case of single group are considered. The numerical examples show that the me...

A Numerical Approach for Solving of Two-Dimensional Linear Fredholm Integral Equations with Boubaker Polynomial Bases

In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...

NON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...

Chained Linear Equating

Linear-Time Approximation Algorithms for Computing Numerical Summation with Provably Small Errors

Given a multiset X = {x1, . . . , xn} of real numbers, the floating-point set summation problem asks for Sn = x1 + · · ·+ xn. Let E n denote the minimum worst-case error over all possible orderings of evaluating Sn. We prove that if X has both positive and negative numbers, it is NP-hard to compute Sn with the worst-case error equal to E n. We then give the first known polynomial-time approxima...