//EXO I


function y=F(x)
    y = cos(x + 3*%pi/8)
endfunction

function y=Fp(x)
    y = -sin(x + 3*%pi/8)
endfunction



x = 0 ;
eps = 1.e-10 ;
nitmax = 100 ;
lambda = 0
k=0

while (abs(F(x)/F(0))>eps)&(k<nitmax)
    x = x - (F(x)*Fp(x))/(lambda + Fp(x)**2)
    k = k+1
end

disp(  x,'x vaut' ) ;
disp(  k,'k vaut' ) ;
//On trouve x = 0.392699 et k = 6 pour lambda = 0.01, k=3 pour lambda = 0

//EXO 2
n=3
x=zeros(n,1)
eps=1.e-10
kmax=100
A=[2,-1,0;-1,2,-1;0,-1,2]
b=[1;1;1]

r=b-A*x
p=r
nr=norm(r)
nr0=nr
k=0

while (nr/nr0)>eps & k<kmax
    q=A*p
    alpha=(r'*r)/(p'*q)
    x=x+(alpha*r)
    rk=r
    r=r-(alpha*q)
    bet=(r'*r)/(rk'*rk)
    p=r+(bet*p)
    nr=norm(r)
    k=k+1

end