Abstract: For finite horizon H∞ filtering problem, the Riccati equation is a nonlinear matrix differential equation and the filtering equation is a linear time-variant one. Furthermore, the existence of the solution to the Riccati equation depends on γ-2. So it is not very easy to solve these equations by general numerical algorithm. According to the analogy between structural mechanics and optimal control, the critical parameter γ-2cr corresponds to the fundamental eigenvalue of a generalized Rayleigh quotient. Therefore, the precise integration method can be employed to solve the Riccati differential equation and to computeγ-2cr with the extended Wittrick-Williams (W-W) algorithm. The numerical solution to the filtering equation can also be obtained by the precise integration method, although it is a time-variant differential equation.