Melina Freitag

Department of Mathematical Sciences

University of Bath

University of Bath

News


Publications

The versions of the papers that can be downloaded from this page represent preliminary versions of the papers and not the final versions published. We advise you to prefer the published articles as they contain the most recent versions.

My author profile in the Bath publication database, in MathSciNet, ZentralblattMATH, SCOPUS, and on GoogleScholar.

Submitted Articles

Articles in Journals

  1. 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)
  2. 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)
  3. 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)
  4. M.A. Freitag, A. Spence:
    A new approach for calculating the real stability radius.
    BIT, 54(2): 381-400, 2014. (article)
  5. 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)
  6. 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)
  7. 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)
  8. 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).
  9. 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)
  10. 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)
  11. 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)
  12. 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)
  13. 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)
  14. 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)
  15. 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)
  16. 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)
  17. 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)
  18. M.A. Freitag, A. Spence:
    Convergence rates for inexact inverse iteration with application to preconditioned iterative solves.
    BIT, 47(1): 27-44, 2007. (link)
  19. 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.
    To appear in 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. 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)
  2. 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).