ME303 Chapter : Direct Iteration Method

• School: University of Waterloo
• Department: Mechanical Engineering
• Course: ME303
• Professor: Serhiy Yarusevych

Document Summary

Convergence of the direct iteration method x = We can show graphically that the iteration will converge only if the function rearrangement that we choose can have a strong effect on convergence of the on. )(xg the right hand side satisfies dg dx. P y=x (slope=1) y=g(x) y y=x y=g(x) root. Calculations: guess x1, compute g(x1, x2= g(x1), i. e. , the length corresponding to x2 equals to the length given by g(x1), as shown on the sketch above. Thus, the point p(x=xnew, y=g(xold) ) falls on the line y=x. In this case, repeating the process moves p along y=x towards the root and the iterations eventually converge, as shown on the sketch. (ii) 1 dg dx y=g(x) y=g(x) y y=x (slope=1) y length=x2 root. In this case, however, repeating the process moves p along y=x away from the root and the iterations do not converge on the root, as shown in the sketch.