A numerical method for solving linear systems in the preconditioned Crank-Nicolson algorithm

摘要

The preconditioned Crank-Nicolson (pCN) algorithm speed-ups the convergence of Markov-Chain-Monte-Carlo methods to high probability zones of target distributions. This method involves the solution of linear systems to propose candidates, which can be critical for a large number of variables to estimate. Thus, this paper proposes an iterative method that avoids the direct inversion of large matrices. The convergence of the proposed numerical method is theoretically proven. Besides, an error bound is provided to approximate candidates with a pre-defined accuracy. Experimental tests are performed on a non-linear Data Assimilation problem and the Lorenz-96 model. The results reveal that the use of our proposed iterative method does not impact the quality of candidates in the pCN method and therefore, posterior errors can be decreased by order of magnitudes for full observational errors. (C) 2020 Elsevier Ltd. All rights reserved.