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A data assimilation process for linear ill-posed problems
- Source :
- Mathematical Methods in the Applied Sciences. 40:5831-5840
- Publication Year :
- 2017
- Publisher :
- Wiley, 2017.
-
Abstract
- In this paper, an iteration process is considered to solve linear ill-posed problems. Based on the randomness of the involved variables, this kind of problems is regarded as simulation problems of the posterior distribution of the unknown variable given the noise data. We construct a new ensemble Kalman filter-based method to seek the posterior target distribution. Despite the ensemble Kalman filter method having widespread applications, there has been little analysis of its theoretical properties, especially in the field of inverse problems. This paper analyzes the propagation of the error with the iteration step for the proposed algorithm. The theoretical analysis shows that the proposed algorithm is convergence. We compare the numerical effect with the Bayesian inversion approach by two numerical examples: backward heat conduction problem and the first kind of integral equation. The numerical tests show that the proposed algorithm is effective and competitive with the Bayesian method. Copyright © 2017 John Wiley & Sons, Ltd.
- Subjects :
- Well-posed problem
Mathematical optimization
General Mathematics
010102 general mathematics
Bayesian probability
Posterior probability
General Engineering
Markov chain Monte Carlo
Inverse problem
01 natural sciences
010101 applied mathematics
symbols.namesake
Data assimilation
symbols
Applied mathematics
Ensemble Kalman filter
0101 mathematics
Randomness
Mathematics
Subjects
Details
- ISSN :
- 01704214
- Volume :
- 40
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi...........7b12b94554ac78451045523b98df12c1