A note on the Karhunen-Loève expansions for infinite-dimensional Bayesian inverse problems

preprint2014arXivOpen access

Abstract

In this note, we consider the truncated Karhunen-Loève expansion for approximating solutions to infinite dimensional inverse problems. We show that, under certain conditions, the bound of the error between a solution and its finite-dimensional approximation can be estimated without the knowledge of the solution.

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