Inverse Linear Problems on Hilbert Space and their Krylov Solvability by Alessandro Michelangeli

Inverse Linear Problems on Hilbert Space and their Krylov Solvability by Alessandro Michelangeli

This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector f in a Hilbert space H, a linear operator A acting on H, and a vector g in H satisfying Af=g, one is interested in approximating f by finite linear combinations of g, Ag, A²g, A³g, … The closed subspace generated by the latter vectors is called the Krylov subspace of H generated by g and A. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text.

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.

“Linear inverse problems constitute a mature research domain with an attractive mathematical theory and fascinating real-world applications… The well-written book presents nice theoretical results, illustrative examples, and encouraging numerical results and should be of interest to the inverse problems community and the researchers in Krylov subspace-based methods.” (Akhtar Khan, zbMATH 1514.65001, 2023)
“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)

Alessandro Michelangeli is at present a von Humboldt Experienced Researcher at the Institute of Applied Mathematics and at the Hausdorff Center for Mathematics at the university of Bonn. His research is at the interface of mathematical physics, functional analysis, partial differential equations, and operator theory, with a special focus on problems and methods for quantum mechanics. He graduated in theoretical physics in Pisa and in mathematical physics at SISSA Trieste, held faculty positions at the LMU Munich and SISSA Trieste, and visiting positions at the University of Cambridge, SISSA Trieste, and Bilkent.

SKU	Unavailable
ISBN 13	9783030881610
ISBN 10	303088161X
Title	Inverse Linear Problems on Hilbert Space and their Krylov Solvability
Author	Alessandro Michelangeli
Series	Springer Monographs In Mathematics
Condition	Unavailable
Binding Type	Paperback
Publisher	Springer Nature Switzerland AG
Year published	2023-02-11
Number of pages	140
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.