title: Meaning of relative tolerance in minimization routine (minpack's hybrd1)
body: <p>I am using a port of minpack's <code>hybrd1</code> in <a href="http://eigen.tuxfamily.org/dox-devel/unsupported/group__NonLinearOptimization__Module.html" rel="nofollow">Eigen</a> which uses <a href="http://en.wikipedia.org/wiki/Powell%27s_method" rel="nofollow">Powell's method</a> to find solution of f(x)=0; the jacobian is computed numerically, in this case.</p>
  
  <p>The solver accepts <code>xtol</code> parameter, relative tolerance, which is by default <code>sqrt(eps)</code> for given numerical type (<code>double</code> in my case)</p>
  
  <p>In most cases, I get satisfactory solution with residuals vector norm like <code>1.446575e-9</code>. Sometimes, though, solution giving norm e.g. 523.543 is accepted, which makes me wonder what the meaning of <code>xtol</code> actually is. What is the reference value against which is the current residuals norm compared?</p>