After giving a broad introduction to the subject, examples and counterexamples of Krylov-solvable and non-solvable inverse problems are provided, together with results on uniqueness of solutions, classes of operators inducing Krylov-solvable inverse problems, and the behaviour of Krylov subspaces under small perturbations. An appendix collects material on weaker convergence phenomena in general projection methods.
This subject of this book lies at the boundary of functional analysis/operator theory and numerical analysis/approximation theory and will be of interest to graduate students and researchers in any of these fields.
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"The material could be used for a single-subject thematic graduate course. Furthermore, it could be used as a reference guide for experts in neighboring fields, such as operator theorists, applied and numerical analysts, etc. ... The monograph ends with an appendix with an outlook on general projection methods and weaker convergence. There is an elaborate list of references and a nice index." (Kees Vuik, Mathematical Reviews, August, 2023)