Publications

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Submitted Articles

• J. König, E. Qian, M.A. Freitag: Dimension and model reduction approaches for linear Bayesian inverse problems with rank-deficient prior covariances (2025) Arxiv link

• I. Daužickaitė, M. A. Freitag, S. Gürol, A. S. Lawless, A. Ramage, J. A. Scott, J. M. Tabeart: An Introduction to Solving the Least-Squares Problem in Variational Data Assimilation (2025) Arxiv link

• T. Okunola, M. Pasha, M. Kilmer, M. Freitag: Efficient Dynamic Image Reconstruction with motion estimation. (2025) Arxiv link 

• M.A. Freitag, J.M. Nicolaus, M. Redmann: Learning Stochastic Reduced Models from Data: A Nonintrusive Approach (2024) Arxiv link

• G. Donval, C. Hand, J. Hook, E. Dupont, M. Sabate Landman , M. Freitag, M. Lennox, T. Düren: Autonomous Exploration and Identification of High Performing Adsorbents using Active Learning (2021). Chemrxiv link 

• M.A. Freitag, D.L.H. Green: Projection methods for weak constraint variational data assimilation. (2019).

Articles in Journals

1. S. Correnty, M.A. Freitag and K. Soodhalter: Chebyshev HOPGD with sparse grid sampling for parameterized linear systems. Calcolo 62(28), 2025 https://doi.org/10.1007/s10092-025-00652-1

2. T. Mach, M.A. Freitag: Solving the Parametric Eigenvalue Problem by Taylor Series and Chebyshev Expansion.   SIAM J. Matrix Anal. Appl., 46(2), 957­‒983, 2025. (link) 

3. M.A. Freitag, J. König, E. Qian: Inference-Oriented Balanced Truncation for Quadratic Dynamical Systems: Formulation for Bayesian Smoothing and Model Stability Analysis. 2024. https://doi.org/10.1002/pamm.202400051

4. A. Kaya, M.A. Freitag 

Low-rank solutions to the stochastic Helmholtz equation. Journal of Computational and Applied Mathematics (2024)

https://doi.org/10.1016/j.cam.2024.115925

5. P.D. Quinn, M.S. Landmann, T. Davis, M.A. Freitag, S. Gazzola, S. Dolgov: Optimal Sparse Energy Sampling for X-ray Spectro-Microscopy: Reducing the X-ray Dose and Experiment Time Using Model Order Reduction. Chem. Biomed. Imaging 2024 DOI: 10.1021/cbmi.3c00116

6. J. König, M.A. Freitag:

Time-limited Balanced Truncation for Data Assimilation Problems. J Sci Comput 97, 47 (2023). https://doi.org/10.1007/s10915-023-02358-4

7. M.A. Freitag, J.M. Nicolaus, M. Redmann: 

Model order reduction methods applied to neural network training. 2023. https://doi.org/10.1002/pamm.202300078

8. M.A. Freitag, P.Kriz,  J.M. Nicolaus, T. Mach, J. M. Nicolaus

Can one hear the depth of  the water? 2023. https://doi.org/10.1002/pamm.202300122

9. J. König, M.A. Freitag: 

Time-limited Balanced Truncation within incremental four-dimensional data assimilation. 2023. https://doi.org/10.1002/pamm.202300019

10. S. Hijazi, M.A. Freitag, N. Landwehr:

POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier-Stokes equations. Adv. Model. Simul. Eng. Sci, 2023. DOI:10.1186/s40323-023-00242-2 link 

11. A. Kaya, M.A. Freitag:
    Conditioning analysis for discrete Helmholtz problems. Comput. Math. with Appl., 118, 2022. (link)

12. M. A. Freitag and S. Reich: Datenassimilation: die nahtlose Verschmelzung von Daten und Modellen. Mitt. Dtsch. Math.-Ver., 30(2):108–112, 2022.

13. M. Redmann, M.A. Freitag:
    Optimization based model order reduction for stochastic systems. Appl. Math. Comput., 398, 2021. (link)

14.  M.A. Freitag:
    Numerical linear algebra in data assimilation. GAMM Mitteilungen, 2020. (link)

15. P. Kürschner, M.A. Freitag:
    Inexact methods for the low rank solution to large scale Lyapunov equations. BIT, 60:1221-1259, 2020. (link)

16. J. Betteridge, J.H. Davenport, M.A. Freitag, W. Heijtljes, S. Kynaston, G. Sankaran, G. Traustason:  Teaching of Computing to Mathematics Students: Programming and Discrete Mathematics. Proceedings of the 3rd Conference on Computing Education Practice, 12, 1-4, 2019 (link)

17. M. Redmann, M.A. Freitag:
    Balanced model order reduction for linear random dynamical systems driven by Lévy noise.  J. Comput. Dyn., 5(1&2): 33-59, 2018. (link)

18. M.A. Freitag, D.L.H. Green:
    A low-rank approach to the solution of weak constraint variational data assimilation problems.  J. Comput. Phys., 357: 263-281, 2018.(link)

19. M.A. Freitag, P. Kürschner, J. Pestana:
    GMRES convergence bounds for eigenvalue problems.  Comput. Methods Appl. Math., 18(2), pp. 203-222, 2018. (link)

20. M.A. Freitag, P. Kürschner:
    Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration.  Numer. Linear Algebra Appl., 22(1):175–196, 2015. (link)

21. S.E. Jenkins, C.J. Budd, M.A. Freitag, N.D. Smith:
    The effect of numerical model error on data assimilation.  J. Comput. Appl. Math., 290:567 – 588, 2015. (link)

22. M.A. Freitag, A Spence, P. Van Dooren:
    Calculating the $H_\infty$-norm using the implicit determinant method.  SIAM J. Matrix Anal. Appl., 35(2), 619-635, 2014. (link)

23. M.A. Freitag, A. Spence:
    A new approach for calculating the real stability radius. BIT, 54(2): 381-400, 2014. (article)

24. R.O. Akinola, M.A. Freitag, A. Spence:
    The computation of Jordan blocks in parameter-dependent matrices.  IMA J. Numer. Anal., 34(3): 955-976, 2014. (article)

25. R.O. Akinola, M.A. Freitag, A. Spence:
    The calculation of the distance to a nearby defective matrix. Numer. Linear Algebra Appl., 21(3): 403-414, 2014. DOI: 10.1002/nla.1888 (article)

26. M.A. Freitag, R.W.E Potthast:
    Synergy of inverse problems and data assimilation techniques. in Large Scale Inverse Problems - Computational Methods and Applications in the Earth Sciences, Radon Ser. Comput. Appl. Math. 13, de Gruyter, 2013. (Preprint)

27. D.P. Almond, C.J. Budd, M.A. Freitag, G.W. Hunt, N.J. McCullen, N.D. Smith:
    The Origin of Power-Law Emergent Scaling in Large Binary Networks. Phys. A, 392(4): 1004-1027, 2013. (link,arxiv).

28. M.A. Freitag, N.K. Nichols, C.J. Budd:
    Resolution of sharp fronts in the presence of model error in variational data assimilation. Q. J. R. Meteorol. Soc. 139: 742-757, 2013. DOI:10.1002/qj.2002 (link)

29. M.A. Freitag, A. Spence:
    A Newton-based method for the calculation of the distance to instability. Linear Alg. Appl., 435(12): 3189-3205, 2011. (article)

30. M.A. Freitag, N.K. Nichols, C.J. Budd:
    Regularization techniques for ill-posed inverse problems in data assimilation. Comput. & Fluids, 46(1): 168-173, 2011. (link)

31. M.A. Freitag, N.K. Nichols, C.J. Budd:
    L1-regularisation for ill-posed problems in variational data assimilation. PAMM, 10(1): 665-668, 2010. (link)

32. M.A. Freitag, A. Spence:
    Shift-invert Arnoldi's method with preconditioned iterative solves. SIAM J. Matrix Anal. Appl., 31(3): 942-969, 2009. (link)

33. M.A. Freitag, A. Spence:
    Rayleigh Quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves. Linear Alg. Appl., 428(8-9): 2049-2060, 2008. (article)

34. M.A. Freitag, A. Spence:
    A tuned preconditioner for inexact inverse iteration applied to Hermitian eigenvalue problems. IMA J. Numer. Anal., 28(3): 522-551, 2008. (link)

35. M.A. Freitag, A. Spence:
    Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem. Electron. Trans. Numer. Anal., 28: 40-64, 2007. (link)

36. M.A. Freitag, K. W. Morton:
    The Preissmann box scheme and its modification for transcritical flows. Internat. J. Numer. Methods Engrg., 70(7): 791-811, 2007. (article)

37. M.A. Freitag, A. Spence:
    Convergence rates for inexact inverse iteration with application to preconditioned iterative solves. BIT, 47(1): 27-44, 2007. (link)

38. M. Freitag, B. Hofmann:
    Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems. J. Inverse Ill-Posed Probl., 13(2): 123-148, 2005. (link)

Books

1. M. Cullen, M.A. Freitag, S. Kindermann and R. Scheichl (Editors):
   Large Scale Inverse Problems: Computational Methods and Applications in the Earth Sciences.
   Radon Series on Computational and Applied Mathematics, Vol. 13, De Gruyter, Berlin (2013). (De Gruyter Link)

2. Melina Freitag:
   The Impact of Multiplication Operators on the Ill-Posedness of Inverse Problems.
   168 pages, VDM Verlag Dr. Müller Aktiengesellschaft & Co. KG (2008). (Available online here)

Theses

1. M.A. Freitag:
   Inner-outer Iterative Methods for Eigenvalue Problems - Convergence and Preconditioning.
   PhD Thesis, Department of Mathematical Sciences, University of Bath (2007). (Gzipped PostScript), (PDF)

2. M. Freitag:
   On the Influence of Multiplication Operators on the Ill-posedness of Inverse Problems.
   Diplomarbeit, Fakultät für Mathematik, Technische Universität Chemnitz (2004). (Available online here)

3. M. Freitag:
   Transcritical flow modelling with the Box Scheme.
   MSc Thesis, Department of Mathematical Sciences, University of Bath (2003). (Gzipped PostScript), (PDF)

Technical reports

1. 1. M. Freitag, P. Kürschner: Inner-outer methods for large-scale two-sided eigenvalue problems; Numerical Solution of PDE Eigenvalue Problems:  Oberwolfach Report 56/2013, 2013

   2. M. Freitag (joint work with A. Spence)
      The calculation of the distance to instability by the computation of a Jordan block.
      Oberwolfach Report No. 37/2009. (Report)

   3. M.A. Freitag, A. Spence, E. Vainikko:
      Rayleigh quotient iteration and simplified Jacobi-Davidson with preconditioned iterative solves for generalised eigenvalue problems.
      (2008). (Gzipped PostScript), (PDF).

Book Review

• M.A. Freitag:
  Model reduction and approximation: theory and algorithms (review of book).
  SIAM Rev. 60 (2018), no. 3, 763–767.