In this paper, we study Projected non-stationary Simultaneous It-erative Reconstruction Techniques (P-SIRT). Based on algorithmic op-erators, convergence result are adjusted with Opial’ s Theorem. The advantages of P-SIRT are demonstrated on examples taken from to-mographic imaging.

There exist many sixth-order Iterative methods for solving nonlinear scalar equations. The purpose of this work is to bring them together. We develop a scheme for unifying sixth-order Iterative methods. Convergence analysis shows that the methods and family of methods, formulated through the scheme are sixth-order convergent. Finally, some computational results are reported to verify the developed theory.

Finding the equilibrium path by non-linear structural analysis is one of the most important subjects in structural engineering. In this way, Incremental-Iterative methods are extremely used. This paper introduces several factors in incremental steps. In addition, it suggests some control criteria for the Iterative part of the non-linear analysis. These techniques are based on the geometric of equilibrium path. Finally, some examples illustrate the capabilities of suggested approaches.

The problem of minimum-cost expansion of power transmission network is formulated as a genetic algorithm with the cost of new lines and security constraints and Kirchhoff’s Law at each bus bar included. A genetic algorithm (GA) is a search or optimization algorithm based on the mechanics of natural selection and genetics. An applied example is presented. The results from a set of tests carried out on the prototype show that the application of GA techniques is feasible in transmission network planning. An empirical analysis of the effects of the parameters of the algorithm is also presented in the context of this novel application. Existing mathematical programming, heuristic techniques, artificial intelligence (AI) and Iterative improvement methods are also reviewed briefly.