function [xvalue,lambda,slambda,xx,sxx,cosangle,residual,tloc] = sampleMinEig(Q,DQ,yMin,yMax,nrSamples,lambdasfem,xsfem);
  %%%% compares the result of stochastic fem with the simulation
tsfem=0;
tsample=0;
n=max(size(Q));
for i=1:nrSamples
  %%%%% draw a random number and scale it;
  omega=-1+(2/nrSamples)*i;
  xvalue(i)=omega;

  t=cputime;
  %spQ=sparse(Q+omega*DQ);
  %nnz(spQ)
  %[U,S]=eigs(spQ,1,'SA');
  [U,S]=eig(Q+omega*DQ);
  tloc(i)=cputime-t
  tsample=tsample+tloc(i);
  
  [lambda(i),index]=min(diag(S));
  x=U(:,index);
  x=x/norm(x);

  t=cputime;
  tic;
  slambda(i)=lambdasfem(1)*Leg0(omega)+lambdasfem(2)*Leg1(omega)+lambdasfem(3)*Leg2(omega)+lambdasfem(4)*Leg3(omega)+lambdasfem(5)*Leg4(omega);
  sx0=xsfem(:,1)*Leg0(omega)+xsfem(:,2)*Leg1(omega);
  sx=sx0+xsfem(:,3)*Leg2(omega)+xsfem(:,4)*Leg3(omega)+xsfem(:,5)*Leg4(omega); 
  residual(i)=norm((Q+omega*DQ)*sx-slambda(i)*sx);
  tloc1=toc
  tsfem=tsfem+tloc1;
  tsample
  tsfem
  if (x'*sx < 0)
    x=-x;
  end 
      xx(:,i)=x;
      sxx(:,i)=sx;
      lxx(:,i)=sx0;
      cosangle(i)=(x'*sx)/(norm(x)*norm(sx));
end
tsample
tsfem