Open problems and perspectives on solving Friedrichs systems by Krylov approximation

2024/06/09 by Noè Angelo Caruso, Caruso, Noe Angelo, Alessandro Michelangeli +1
Computer Science · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2406.05777

openalex publication_date 2024/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We set up, at the abstract Hilbert space setting, the general question on when an inverse linear problem induced by an operator of Friedrichs type admits solutions belonging to (the closure of) the Krylov subspace associated to such operator. Such Krylov solvability of abstract Friedrichs systems allows to predict when, for concrete differential inverse problems, truncation algorithms can or cannot reproduce the exact solutions in terms of approximants from the Krylov subspace.

Related

• Inverse linear problems on Hilbert space and their Krylov solvability
• On Krylov solutions to infinite-dimensional inverse linear problems
• Krylov solvability under perturbations of abstract inverse linear problems
• Krylov solvability of unbounded inverse linear problems
• Compound Krylov subspace methods for parametric linear systems