Residual Smoothing Techniques for Iterative Methods

Residual Smoothing Techniques for Iterative Methods

An iterative method for solving a linear system Ax b produces iterates {xk with associated residual norms that, in general, need not decrease "smoothly" to zero. "Residual smoothing" techniques are considered that generate a second sequence {Yk via a simple relation yk (1 0k)yk-+ r/kxk. The authors first review and comment on a technique of this form introduced by Sch6nauer and Weiss that resul...

Residual Smoothing Techniques: Do They Improve the Limiting Accuracy of Iterative Solvers?

Minimal Residual Smoothing in Multi-Level Iterative Method

Minimal Residual Smoothing in Multi-Level Iterative Method

A minimal residual smoothing (MRS) technique is employed to accelerate the convergence of the multi-level iterative method by smoothing the residuals of the original iterative sequence. The sequence with smoothed residuals is reintroduced into the multi-level iterative process. The new sequence generated by this acceleration procedure converges much faster than both the sequence generated by th...

Network Planning Using Iterative Improvement Methods and Heuristic Techniques

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 ...