Matrix-free stochastic calculation of operator norms without using adjoints
This paper considers the problem of computing the operator norm of a linear map between finite dimensional Hilbert spaces when only evaluations of the linear map are available and under restrictive storage assumptions. We propose a stochastic method of random search type for the maximization of the...
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Zusammenfassung: | This paper considers the problem of computing the operator norm of a linear
map between finite dimensional Hilbert spaces when only evaluations of the
linear map are available and under restrictive storage assumptions.
We propose a stochastic method of random search type for the maximization of
the Rayleigh quotient and employ an exact line search in the random search
directions.
Moreover, we show that the proposed algorithm converges to the global maximum
(the operator norm) almost surely and illustrate the performance of the method
with numerical experiments. |
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DOI: | 10.48550/arxiv.2410.08297 |