Rational Krylov subspaces have become a fundamental ingredient in numerical linear algebra methods associated with reduction strategies. Nonetheless, many structural properties of the reduced matrices in these subspaces are not fully understood. We advance in this analysis by deriving bounds on the entries of rational Krylov reduced matrices and of their functions, that ensure an a-priori decay of their entries as we move away from the main diagonal. As opposed to other decay pattern results in the literature, these properties hold in spite of the lack of any banded structure in the considered matrices. Numerical experiments illustrate the quality of our results.

有理Krylov子空间已成为与归约策略相关的数值线性代数方法的基本要素。但是，这些子空间中的简化矩阵的许多结构特性尚未完全了解。我们通过推导有理Krylov约化矩阵及其函数的边界来推进此分析，当我们远离主对角线时，这些矩阵可确保它们的项先验衰减。与文献中的其他衰减模式结果相反，尽管考虑的矩阵中没有任何带状结构，但这些属性仍然成立。数值实验说明了我们的结果的质量。