Computing adjoint mismatch of linear maps
Numerical Analysis
2026-03-10 v2 Numerical Analysis
Optimization and Control
Abstract
This paper considers the problem of detecting adjoint mismatch for two linear maps. To clarify, this means that we aim to calculate the operator norm for the difference of two linear maps, where for one we only have a black-box implementation for the evaluation of the map, and for the other we only have a black-box for the evaluation of the adjoint map. We give a stochastic algorithm for which we prove the almost sure convergence to the operator norm. The algorithm is a random search method for a generalization of the Rayleigh quotient and uses optimal step sizes. Additionally, a convergence analysis is done for the corresponding singular vector and the respective eigenvalue equation.
Cite
@article{arxiv.2503.21361,
title = {Computing adjoint mismatch of linear maps},
author = {Jonas Bresch and Dirk A. Lorenz and Felix Schneppe and Maximilian Winkler},
journal= {arXiv preprint arXiv:2503.21361},
year = {2026}
}