// TP_NL1_vp.sce
//
A = [2 -1 0; ...
     -1 2 -1; ...
     0 -1  2];
    
function Fres = Fvpropre(X)
    xvec = X(1:3);
    lambda = X(4);
    Fres = zeros(4,1);
    Fres(1:3) = A*xvec - lambda * xvec;
    Fres(4)   = xvec'*xvec-1; // norm(xvec)^2 - 1; 
endfunction

// X0 = ([1;1;1], 1) => lambda=0.5857
// X0 = ([1;-10;10], 0) => lambda=2
// X0 = ([-1;1;-1], -1]) = lambda=3.41
x0vec = [-1;1;-1]; 
lambda0 = -1;
X0 = [x0vec; lambda0];

Xsol = fsolve(X0, Fvpropre);
xvec = Xsol(1:3)
lambda = Xsol(4)

// Verification avec spec(A)
[R, D] = spec(A)

//