This paper presents numerical methods for solving the Modified Filter Algebraic Riccati Equation (MFARE) for synthesis of H-infinity fault detection filters. Two methods are presented, namely the gamma-iteration and then rewriting the MFARE in Linear Matrix Inequalities (LMIs) and casting it as a convex optimization problem. Each algorithm has to ensure the condition for a global convergence and also has to deliver an optimal solution. Not at least the computational cost has to be as small as possible.