Inverse Linear Problems on Hilbert Space and their Krylov Solvability (eBook)
XI, 140 Seiten
Springer International Publishing (Verlag)
978-3-030-88159-7 (ISBN)
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.
Noè Angelo Caruso is a postdoctoral researcher at the Gran Sasso Science Institute (GSSI) in L'Aquila, and a recent PhD graduate in Mathematical Analysis, Modelling and Applications from the International School of Advanced Studies (SISSA) in Trieste. His research interests are in operator theory and abstract approximation theory, taking inspiration from topics in theoretical numerical analysis with a particular emphasis on underlying functional analytic aspects.
?Alessandro Michelangeli is the Alexander von Humboldt Experienced Researcher at the Institute for Applied Mathematics and the Hausdorff Center for Mathematics, University of Bonn. After obtaining his PhD in mathematical physics from SISSA, Trieste, he was a post-doc and then assistant professor at Ludwig Maximilians University, Munich (2007-2015). He has held numerous other post-doctoral and visiting positions, including at Cambridge University, SISSA, and CIRM (Trento). His research focuses on mathematical methods in physics, and the rigorous operator-theoretic understanding of numerical algorithms. In 2017 he was awarded the Alexander Vasiliev Award for an outstanding paper published in Analysis and Mathematical Physics.
Erscheint lt. Verlag | 10.2.2022 |
---|---|
Reihe/Serie | Springer Monographs in Mathematics | Springer Monographs in Mathematics |
Zusatzinfo | XI, 140 p. 8 illus. in color. |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Mathematik |
Schlagworte | bounded linear operators • conjugate gradient methodsspectral measures • cyclic operators • cyclic vectors • hausdorff distance • ill-posed problems • infinite-dimensional Hilbert space • inverse linear problems on Hilbert space • Krylov solution • Krylov solvability • Krylov subspaces • orthogonal polynomials • orthonormal basis discretization • self-adjoint operators • spectral theory • subspace perturbations • unbounded operators on Hilbert space |
ISBN-10 | 3-030-88159-8 / 3030881598 |
ISBN-13 | 978-3-030-88159-7 / 9783030881597 |
Haben Sie eine Frage zum Produkt? |
![PDF](/img/icon_pdf_big.jpg)
Größe: 2,0 MB
DRM: Digitales Wasserzeichen
Dieses eBook enthält ein digitales Wasserzeichen und ist damit für Sie personalisiert. Bei einer missbräuchlichen Weitergabe des eBooks an Dritte ist eine Rückverfolgung an die Quelle möglich.
Dateiformat: PDF (Portable Document Format)
Mit einem festen Seitenlayout eignet sich die PDF besonders für Fachbücher mit Spalten, Tabellen und Abbildungen. Eine PDF kann auf fast allen Geräten angezeigt werden, ist aber für kleine Displays (Smartphone, eReader) nur eingeschränkt geeignet.
Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen dafür einen PDF-Viewer - z.B. den Adobe Reader oder Adobe Digital Editions.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen dafür einen PDF-Viewer - z.B. die kostenlose Adobe Digital Editions-App.
Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.
aus dem Bereich