We set up, at the abstract Hilbert space setting, the general question on when an inverse linear problem induced by an operator of Friedrichs type admits solutions belonging to (the closure of) the Krylov subspace associated to such operator. Such Krylov solvability of abstract Friedrichs systems allows to predict when, for concrete differential inverse problems, truncation algorithms can or cannot reproduce the exact solutions in terms of approximants from the Krylov subspace.

翻译：我们在抽象希尔伯特空间框架下，建立了一个一般性问题：由弗里德里希斯型算子诱导的逆线性问题何时存在属于该算子对应Krylov子空间（或其闭包）的解。此类抽象弗里德里希斯系统的Krylov可解性，能够预测具体微分逆问题中截断算法是否可以通过Krylov子空间的逼近元精确重构解。