An overview of model reduction methods and a new result

Model reduction methods can be classified in two broad categories, namely, SVD- (Singular Value Decomposition) based methods and Krylov-based or moment matching methods. As each one of these categories has advantages and disadvantages, a third category named SVD-Krylov aims to combine their best attributes. Balanced truncation (BT) falls into the first category of reduction methods. In this note after a brief overview of model reduction methods, we will establish a link between BT and Krylov projection methods by explicitly deriving Krylov projectors which achieve balanced truncation. In other words we will show that BT can be achieved by rational interpolation at appropriately determined points of the complex plane.