A Gradient Projection Algorithm for Relaxation Methods
A Gradient Projection Algorithm for Relaxation Methods
J L Mohammed
The book A Gradient Projection Algorithm for Relaxation Methods was written by author J L Mohammed Here you can read free online of A Gradient Projection Algorithm for Relaxation Methods book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is A Gradient Projection Algorithm for Relaxation Methods a good or bad book?
What reading level is A Gradient Projection Algorithm for Relaxation Methods book?
To quickly assess the difficulty of the text, read a short excerpt:
Combining, we have shown that w £ F^ . But X ■^ ^ V V 1 q'w= ) q. V. + ) q. (v. + rrr;— v. ) N = q-v + (t^-qi)v^ > q-v, since i e S implies q. 0. This is a contradiction, since q*v is maximum among v e F^ . Thus we must have v. = for i e S„. That is, v e W. 1 N Theorem; The output vector u solves Problem P. Proof : According to the lemma, it suffices to show that u e F^, and q*u >_ q«v for all v e W n f^. -10- Clearly, y calculated in step 3 of the algorithm satisfies y. = for i e Sj^. Further..., if i e D, i ft S^, then q^ >^ t^ according to the definition of S, and so y . = q . - t^ > . So y. > for all i e D. Finally Ey, = by direct computation. Thus y e W. In fact, as can be easily seen, step 3 merely performs an orthogonal projection of q onto the subspace W. That is, for any v e W, -v - . A ^bxt:. '' (q - y) . V = 0. ;oqo- . TO. R. J;;.. :. So q«v = y«v for all v e W. The output vector u calculated in step 4 is simply a length normalization of y, and so u is in W also.
User Reviews: