Inverse Linear Problems on Hilbert Space and their Krylov Solvability
Inverse Linear Problems on Hilbert Space and their Krylov Solvability
English | 2021 | ISBN: 303088158X | 150 Pages | PDF | 2 MB
English | 2021 | ISBN: 303088158X | 150 Pages | PDF | 2 MB
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.