We analyzed the rate of convergence of a new modified interval symmetric single-step procedure ISS2-5D which is an extension from the previous procedure ISS2. The algorithm of ISS2-5D includes the introduction of reusable correctors δi(k) (i = 1, ..., n) for k ≥ 0. Furthermore, this procedure was tested on five test polynomials and the results were obtained using MATLAB 2007 software in association with IntLab V5.5 toolbox to record the CPU times and the number of iterations.
Data envelopment analysis (DEA) is a mathematical programming for evaluating the relative efficiency of decision making units (DMUs). The first DEA model (CCR model) assumed for exact data, later some authors introduced the applications of DEA which the data was imprecise. In imprecise data envelopment analysis (IDEA) the data can be ordinal, interval and fuzzy. Data envelopment analysis also can be used for the future programming of organizations and the response of the different policies, which is related to the target setting and resource allocation. The existing target model that conveys performance based targets in line with the policy making scenarios was defined for exact data. In this paper we improved the model for imprecise data such as fuzzy, ordinal and interval data. To deal with imprecise data we first established an interval DEA model. We used one of the methods to convert fuzzy and ordinal data into the interval data. A numerical experiment is used to illustrate the application to our interval model.
The nonlinear conjugate gradient (CG) methods have widely been used in solving unconstrained optimization problems. They are well-suited for large-scale optimization problems due to their low memory requirements and least computational costs. In this paper, a new diagonal preconditioned conjugate gradient (PRECG) algorithm is designed, and this is motivated by the fact that a pre-conditioner can greatly enhance the performance of the CG method. Under mild conditions, it is shown that the algorithm is globally convergent for strongly convex functions. Numerical results are presented to show that the new diagonal PRECG method works better than the standard CG method.