% algorithme de minimisation de 1/2 x'*A*x-x'*b par
% méthode de la plus forte pente (Steepest Descent)
function [x,residus] = SD(A,b,x,niter_max,tolerance)

n=length(b);
residus=zeros(n,1);

r=b-A*x;
rold=r'*r;

residus(1,1)=sqrt(rold);

for i=1:niter_max
    alpha=rold/(r'*A*r);
    x=x+alpha*r;
    r=b-A*x;
    rnew=r'*r;
    residus(i+1,1)=sqrt(rnew);
    if residus(i+1,1)<tolerance
        break;
    end
    rold=rnew;
end