希尔伯特空间上的线性反问题及其Krylov可解性
Inverse linear problems on Hilbert space and their Krylov solvability
摘要：
这本专著是集中在三个数学主题的交叉点，这是理论性的，但与动机和相关性深深植根于应用：线性逆问题的抽象，在一般无限维希尔伯特空间;的概念Krylov子空间相关的逆问题，即，通过反复应用线性算子建立在反问题的数据上的循环子空间;通过Krylov子空间方法解决反问题的可能性，即投影方法，其中相对于Krylov子空间进行有限维截断，并且逼近收敛到反问题的精确解。
英文摘要：
This monograph is centred at the intersection of three mathematical topics, that are theoretical in nature, yet with motivations and relevance deep rooted in applications: the linear inverse problems on abstract, in general infinite-dimensional Hilbert space; the notion of Krylov subspace associated to an inverse problem, i.e., the cyclic subspace built upon the datum of the inverse problem by repeated application of the linear operator; the possibility to solve the inverse problem by means of Krylov subspace methods, namely projection methods where the finite-dimensional truncation is made with respect to the Krylov subspace and the approximants converge to an exact solution to the inverse problem.
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