The Fundamental Subspaces of Ensemble Kalman Inversion
Elizabeth Qian, Christopher Beattie

TL;DR
This paper analyzes the convergence behavior of Ensemble Kalman Inversion (EKI) methods for linear inverse problems by introducing fundamental subspaces, providing spectral decompositions, and verifying convergence rates through numerical experiments.
Contribution
It introduces a new analysis of EKI's convergence using fundamental subspaces, offering spectral decompositions and insights into deterministic and stochastic EKI behavior.
Findings
Verifies convergence rates for EKI in linear settings.
Defines six fundamental subspaces for EKI analysis.
Provides spectral decompositions linking EKI to linear algebra fundamentals.
Abstract
Ensemble Kalman Inversion (EKI) methods are a family of iterative methods for solving weighted least-squares problems, especially those arising in scientific and engineering inverse problems in which unknown parameters or states are estimated from observed data by minimizing the weighted square norm of the data misfit. Implementation of EKI requires only evaluation of the forward model mapping the unknown to the data, and does not require derivatives or adjoints of the forward model. The methods therefore offer an attractive alternative to gradient-based optimization approaches in inverse problem settings where evaluating derivatives or adjoints of the forward model is computationally intractable. This work presents a new analysis of the behavior of both deterministic and stochastic versions of basic EKI for linear observation operators, resulting in a natural interpretation of EKI's…
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Taxonomy
TopicsInertial Sensor and Navigation · Target Tracking and Data Fusion in Sensor Networks
