function [x,k,err]=Newton(B1,B2,b1,b2,x0,eps,kmax)
//- Methode de Newton pour resoudre max(B1 x-b1,B2 x-b2)=0;

//- Initialisations:
k=0;
x=x0;
err=eps+1;

Fp=spzeros(B1);
Id=speye(B1); 
PRINT=0

while( k<kmax & err>eps )
  
  k=k+1 

  xold=x;

  //- Definition de F'(x):
  test=(B1*x-b1) - (B2*x-b2); 
  i=find(test>=0); Fp(i,:)=B1(i,:);
  j=find(test<0);  Fp(j,:)=B2(j,:);
  F=max(B1*x-b1,B2*x-b2);

  //- Definition nouvel x
  x=x-Fp\F;
 
  //- Estimateur pour convergence
  err=norm(max(B1*x-b1,B2*x-b2),'inf');

  if PRINT
    printf('k=%5i, err=%12.6f, n(x-xold)=%10.6f\n',k,err,norm(x-xold)); 
    //scanf('%c');
  end

end

endfunction