Inverse Linear Problems On A Hilbert Space And Their Krylov Solvability
Download Inverse Linear Problems On A Hilbert Space And Their Krylov Solvability PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Inverse Linear Problems On A Hilbert Space And Their Krylov Solvability book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Inverse Linear Problems on a Hilbert Space and Their Krylov Solvability
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.
Inverse Linear Problems on Hilbert Space and their Krylov Solvability
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.
Singularities, Asymptotics, and Limiting Models
This present book collects a distinguished selection of contributions by scholars who participated as speakers or as visiting scientists in the intensive programme Puglia Summer Trimester 2023 took place in Bari, Italy, from April to July 2023, and also includes contributions by further scholars who are expert in related fields. The programme was structured around a series of main meetings, including a general conference and a summer school, supplemented by the local presence and activities of an amount of visiting scientists. Additionally, efforts were made to disseminate and popularise mathematics among schools and the general public, with the aim of extending the programme's impact beyond the immediate academic sphere. Each chapter, in the form of retrospective reviews, overviews on recent developments, announcements and comments of new results, as well as outlooks on future perspectives, represents some of the main scientific instances of the trimester in Bari. The trimester was actually focussed on a spectrum of mathematical problems, directly stemming or inspired from a variety of physical domains, involving singular modelling, asymptotic and emergent phenomena, singular interactions, non-trivial limit effects. Natural backgrounds are quantum physics, cold atom physics, soft matter physics, with methods and tools, suitably adapted to such singular settings, spanning across operator and spectral theory, functional analysis, probability, differential geometry, partial differential equations, and numerical analysis.