TD2 - Espace d`authentification univ

f(u, v) = 1 −1
1 + au2+v2
a > 0a= 0.5
f
x1x1= (2.5,2.5)
k∈ {1,2, ...}
dk
αk
xk+1 =xk+αkdk
αk=α αk
α7→ f(xk+αdk)
kf0(xk)k< tol tol
tol = 10−5f0f
f
a= 1
f0(x)f
x f f
α
α

−3 −1 0 1 2 3
−3 −1 0 1 2 3
f xk
α= 1 x0= (2.5,2.5)
(0,0)
dk
xk+1
dk=−(f00(xk))−1f0(xk)
f00 α= 1
f00(x)
f x f f
x1= (2.5,2.5) x1= (0.1,0.1)
f(u, v) = (1 −u)2+ 100(v−u2)2.