Noe Angelo Caruso,Alessandro Michelangeli
Inverse Linear Problems on Hilbert Space and their Krylov Solvability
Inverse Linear Problems on Hilbert Space and their Krylov Solvability
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- More about Inverse Linear Problems on Hilbert Space and their Krylov Solvability
The book discusses the theory of abstract inverse linear problems on Hilbert space, focusing on approximating unknown vectors by finite linear combinations of known vectors using projection methods on the Krylov subspace. It provides examples and counterexamples, discusses uniqueness of solutions, and explores the behaviour of Krylov subspaces under perturbations.
Format: Hardback
Length: 140 pages
Publication date: 11 February 2022
Publisher: Springer Nature Switzerland AG
This comprehensive book delves into the intricate realm of abstract inverse linear problems on Hilbert spaces. It begins by introducing the fundamental concepts and assumptions required for the study of these problems. The author then presents a detailed discussion of the theory, encompassing various methods and techniques for approximating unknown vectors by finite linear combinations of known vectors.
The Krylov subspace, a crucial concept in this field, is introduced, representing the closed subspace generated by a given vector and a linear operator. The primary focus of the text revolves around the possibility of solving these inverse problems using projection methods on the Krylov subspace.
Throughout the book, examples and counterexamples are provided to illustrate the principles and applications of Krylov-solvable and non-solvable inverse problems. The results cover topics such as uniqueness of solutions, classes of operators that induce Krylov-solvable inverse problems, and the behaviour of Krylov subspaces under small perturbations. An appendix is included to gather additional material on weaker convergence phenomena in general projection methods.
This book appeals to graduate students and researchers in functional analysis/operator theory, numerical analysis/approximation theory, and related fields. Its comprehensive coverage and analytical approach make it an invaluable resource for those seeking to advance their understanding of abstract inverse linear problems and their practical applications.
Weight: 401g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030881580
Edition number: 1st ed. 2021
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