Curve fit - use the analytical hessian to calculate the uncertainty

Hi! I have a question about least square fits. Is there some light weight/fast least square method that i can use that does not calculate the numerical covariance, i.e. waist calculations on this, so I can just use the analytical hessian to get the covariance matrix, to then calculate the uncertainty for the fit? The idea is to compare with methods like curve_fit() and calculate the variance from the Jacobian and the returned numerical covariance matrix?