| OCR Text |
Show 62 each each iteration at is technique it to make to at was only the the maximum in a sure that f(u) the for where than each at on to Since is downhill This started. we is is larger choice our if a guaranteed are we decrease the in monitoring step "uphill" direction by f(u) Newton a going uphill iteration better the at really doing be might we Thus landed below function, however, f". reason and smeller previous step. the always proceed du, since step be to not, are positive of region than We step. previous If'(u)1 expect we step we overshot of slope of illustrated the in figure 13. - - -.., - I I Figure Thus 13 Overshooting - f(ui+1)<f(ui) if The the dUe we algorithm wh i I elf I can now (u) I damp the u Note which the addition exits if of du = u the iteration by halving > E then else while Maximum becomes f" (u) <0 if Local f(u+du)<f(u) du=du/2 if I du 1< t.z. + I du=-f (u) If" (u) ' d u= f (u) return du escape clause in the gets exceedingly small. damping This has loop proven |
