Inverse Linear Problems on Hilbert Space and their Krylov Solvability / by Noè Angelo Caruso, Alessandro Michelangeli.

Format:

Book

Author/Creator:

Noè Angelo Caruso, author.

Michelangeli, Alessandro, author.

Series:

Springer Monographs in Mathematics, 2196-9922

Language:

English

Subjects (All):

Differential equations.

Functional analysis.

Numerical analysis.

Operator theory.

Differential Equations.

Functional Analysis.

Numerical Analysis.

Operator Theory.

Local Subjects:

Differential Equations.

Functional Analysis.

Numerical Analysis.

Operator Theory.

Physical Description:

1 online resource (150 pages)

Edition:

1st ed. 2021.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2021.

Summary:

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. .

Contents:

Introduction and motivation

Krylov solvability of bounded linear inverse problems

An analysis of conjugate-gradient based methods with unbounded operators

Krylov solvability of unbounded inverse problems

Krylov solvability in a perturbative framework

Outlook on general projection methods and weaker convergence

References

Index.

Notes:

Includes bibliographical references and index.

Other Format:

Print version: Caruso, Noè Angelo Inverse Linear Problems on Hilbert Space and Their Krylov Solvability

ISBN:

3-030-88159-8

OCLC:

1302008344