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## References
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To implement the various versions of the DMD algorithm we follow these works:
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### General DMD References
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* Kutz, Brunton, Brunton, Proctor. *Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems*. SIAM Other Titles in Applied Mathematics, 2016. [[DOI](https://doi.org/10.1137/1.9781611974508)][[bibitem](readme/refs/Kutz2016_1.bib)].
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*Gavish, Donoho. *The optimal hard threshold for singular values is 4/sqrt(3)*. IEEE Transactions on Information Theory, 2014. [[DOI](https://doi.org/10.1109/TIT.2014.2323359)][[bibitem](readme/refs/Gavish2014.bib)].
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* Matsumoto, Indinger. *On-the-fly algorithm for Dynamic Mode Decomposition using Incremental Singular Value Decomposition and Total Least Squares*. 2017. [[arXiv](https://arxiv.org/abs/1703.11004)][[bibitem](readme/refs/Matsumoto2017.bib)].
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* Hemati, Rowley, Deem, Cattafesta. *De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets*. Theoretical and Computational Fluid Dynamics, 2017. [[DOI](https://doi.org/10.1007/s00162-017-0432-2)][[bibitem](readme/refs/Hemati2017.bib)].
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*Brunton, Budišić, Kaiser, Kutz. *Modern Koopman Theory for Dynamical Systems*. SIAM Review, 2022. [[DOI](https://doi.org/10.1137/21M1401243)][[bibitem](readme/refs/Brunton2022.bib)].
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### DMD Variants: Noise-robust Methods
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* Dawson, Hemati, Williams, Rowley. *Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition*. Experiments in Fluids, 2016. [[DOI](https://doi.org/10.1007/s00348-016-2127-7)][[bibitem](readme/refs/Dawson2016.bib)].
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* Hemati, Rowley, Deem, Cattafesta. *De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets*. Theoretical and Computational Fluid Dynamics, 2017. [[DOI](https://doi.org/10.1007/s00162-017-0432-2)][[bibitem](readme/refs/Hemati2017.bib)].
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* Héas, Herzet. *Low-rank dynamic mode decomposition: An exact and tractable solution*. Journal of Nonlinear Science, 2022. [[DOI](https://doi.org/10.1007/s00332-021-09770-w)][[bibitem](readme/refs/Heas2022.bib)].
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* Takeishi, Kawahara, Yairi. *Subspace dynamic mode decomposition for stochastic Koopman analysis*. Physical Review E, 2017. [[DOI](https://doi.org/10.1103/PhysRevE.96.033310)][[bibitem](readme/refs/Takeishi2017.bib)].
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* Baddoo, Herrmann, McKeon, Kutz, Brunton. *Physics-informed dynamic mode decomposition*. Proceedings of the Royal Society A, 2023. [[DOI](https://doi.org/10.1098/rspa.2022.0576)][[bibitem](readme/refs/Baddoo2023.bib)].
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* Askham, Kutz. *Variable projection methods for an optimized dynamic mode decomposition*. SIAM Journal on Applied Dynamical Systems, 2018. [[DOI](https://doi.org/10.1137/M1124176)][[bibitem](readme/refs/Askham2018.bib)].
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* Sashidhar, Kutz. *Bagging, optimized dynamic mode decomposition for robust, stable forecasting with spatial and temporal uncertainty quantification*. Proceedings of the Royal Society A, 2022. [[DOI](https://doi.org/10.1098/rsta.2021.0199)][[bibitem](readme/refs/Sashidhar2022.bib)].
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### DMD Variants: Additional Methods and Extensions
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* Proctor, Brunton, Kutz. *Dynamic mode decomposition with control*. SIAM Journal on Applied Dynamical Systems, 2016. [[DOI](https://doi.org/10.1137/15M1013857)][[bibitem](readme/refs/Proctor2016.bib)].
* Williams, Rowley, Kevrekidis. *A kernel-based method for data-driven koopman spectral analysis*. Journal of Computational Dynamics, 2015. [[DOI](https://doi.org/10.3934/jcd.2015005)][[bibitem](readme/refs/Williams2015.bib)].
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* Baddoo, Herrmann, McKeon, Brunton. *Kernel learning for robust dynamic mode decomposition: linear and nonlinear disambiguation optimization*. Proceedings of the Royal Society A, 2022. [[DOI](https://doi.org/10.1098/rspa.2021.0830)][[bibitem](readme/refs/Baddoo2022.bib)].
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### Implementation Tools and Preprocessors
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* Gavish, Donoho. *The optimal hard threshold for singular values is 4/sqrt(3)*. IEEE Transactions on Information Theory, 2014. [[DOI](https://doi.org/10.1109/TIT.2014.2323359)][[bibitem](readme/refs/Gavish2014.bib)].
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* Matsumoto, Indinger. *On-the-fly algorithm for Dynamic Mode Decomposition using Incremental Singular Value Decomposition and Total Least Squares*. 2017. [[arXiv](https://arxiv.org/abs/1703.11004)][[bibitem](readme/refs/Matsumoto2017.bib)].
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* Hirsh, Harris, Kutz, Brunton. *Centering data improves the dynamic mode decomposition*. SIAM Journal on Applied Dynamical Systems, 2020. [[DOI](https://doi.org/10.1137/19M1289881)][[bibitem](readme/refs/Hirsh2020.bib)]
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### Recent works using PyDMD
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You can find a list of the scientific works using **PyDMD**[here](https://scholar.google.com/scholar?oi=bibs&hl=en&cites=5544023489671534143).
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