We present the first formulation of the optimal polynomial approximation of the solution of linear non-autonomous systems of ODEs in the framework of the so-called $\star$-product. This product is the basis of new approaches for the solution of such ODEs, both in the analytical and the numerical sense. The paper shows how to formally state the problem and derives upper bounds for its error.

翻译：本文首次在所谓的$\star$-积框架下，提出了线性非自治常微分方程组解的最优多项式逼近的表述。该乘积是求解此类常微分方程的新方法的基础，无论是在解析意义还是数值意义上。本文展示了如何形式化地表述该问题，并推导了其误差的上界。