Speaker
Description
In this talk, we address the challenge of determining the norm of a linear operator solely by evaluating it. This problem naturally arises whenever the adjoint is not known and cannot be attained. After giving an overview of algorithms fitted to this problem, we propose an algorithm that employs a semi-stochastic approach to iteratively refine the estimate, achieving almost sure convergence to the true norm. Beginning with the underlying problem, we will explore the construction of an algorithm that requires only oracle access to the operators, avoids explicit matrix storage and ensures minimal memory usage. We will calculate optimal step sizes and provide a visual depiction of the proof of almost sure convergence. Numerical experiments demonstrate the practical efficiency of the method across various scenarios, highlighting its potential applications whenever adjoint consistency cannot be guaranteed.
