Computing adjoint mismatch of linear maps

Journal of Computational and Applied Mathematics 2026 Open access

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Authors: Jonas Bresch, Dirk A. Lorenz, Felix Schneppe, Maximilian Winkler
DOI: 10.1016/j.cam.2026.117853
Cited by: 0
References: 26

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.

Fields of Study & Subjects

Advanced Topics in Algebra Polynomial and algebraic computation Matrix Theory and Algorithms

Publication details

Journal / source
Journal of Computational and Applied Mathematics
Publisher
Elsevier BV
Volume
488
Pages
117853–117853
Publication date
1 June 2026
Language
EN