Close approximations of ideal linear transforms, such as the forward and inverse discrete cosine transformation (DCT), are formed with minimum complexity using fixed-point arithmetic. The transformation is decomposed into a smaller set of transformations (e.g., the LLM decomposition of the DCT). The multiplication factors of the decomposition are then approximated by a fixed-point representation. However, instead of simply applying scaling and rounding operations to produce fixed-point approximations closest to the multiplication factors themselves, fixed-point multiplication factors are chosen that have the effect (after the cascaded operations of the various stages of decomposition) of being the closest feasible approximations of the entries in the resulting complete ideal transformation matrix.