In this paper we consider the optimal L(2) model reduction problem where the plant model depends on parameters that are measurable. Such cases occur in many on-line as well as off-line applications and the question that arises is how to update the reduced order model without complete re-solution of the problem. A method of approximation of the updated reduced-order model, which is based on its series expansion, is given. A similar approach is used to develop a new algorithm for the numerical solution of the nominal problem. The algorithm compares well, in terms of computation effort and convergence properties, with homotopic methods which are the common way of solving the equations.