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：本文在所谓的$\star$-积框架下，首次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形式。该乘积是解析和数值意义上求解此类常微分方程新方法的基础。本文展示了如何正式表述该问题，并推导了其误差的上界。