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 project