function [x,residues] = CGk(A,b,x,tolerance,k)

n=length(b);
residues=zeros(n+1,1);
P=zeros(n,n);

r=b-A*x;
residues(1,1)=r'*r;

for i=1:n
    somme=zeros(n,1);
    for j=i-1:-1:i-k%projection sur k directions anterieures
        if(j>=1)
            pj=P(:,j);
            somme=somme+r'*A*pj/(pj'*A*pj)*pj;
        else
            break;
        end
    end
    p=r-somme;
    P(:,i)=p;
    %alpha=p'*b/(p'*A*p);
    alpha=p'*r/(p'*A*p);
    x=x+alpha*p;
    r=b-A*x;
    residues(i+1,1)=sqrt(r'*r);
    if(residues(i+1,1)<tolerance)
        break;
    end
end