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Prof. Dr. Melina Freitag

Professorin

Kontakt
Raum:
2.09.2.09
Telefon:
+49 331 977-203121
E-Mail:
melina.freitag@uni-potsdam.de
...

Persönliche Seite

Research interests

  • Numerical linear algebra, in particular iterative methods for eigenvalue problems and linear systems, Krylov subspace methods.
  • Model order reduction, matrix theory and applications.
  • Data assimilation and inverse problems.

Publications

2021 | Optimization based model order reduction for stochastic systems | M. Redmann, M.A. FreitagZeitschrift: Appl. Math. Comput., 398Link zur Publikation

Optimization based model order reduction for stochastic systems

Autoren: M. Redmann, M.A. Freitag (2021)

Zeitschrift:
Appl. Math. Comput., 398

2020 | Inexact methods for the low-rank solution to large-scale Lyapunov equations | P. Kürschner, M.A. FreitagZeitschrift: BIT, 60:1221-1259Link zur Publikation , Link zum Preprint

Inexact methods for the low-rank solution to large-scale Lyapunov equations

Autoren: P. Kürschner, M.A. Freitag (2020)

Zeitschrift:
BIT, 60:1221-1259

2020 | Numerical linear algebra in data assimilation | M.A. FreitagZeitschrift: GAMM MitteilungenLink zur Publikation

Numerical linear algebra in data assimilation

Autoren: M.A. Freitag (2020)

Zeitschrift:
GAMM Mitteilungen

2019 | Teaching of Computing to Mathematics Students: Programming and Discrete Mathematics | J. Betteridge, J.H. Davenport, M.A. Freitag, W. Heijtljes, S. Kynaston, G. Sankaran, G. TraustasonZeitschrift: Proceedings of the 3rd Conference on Computing Education Practice, 12, 1-4Link zur Publikation

Teaching of Computing to Mathematics Students: Programming and Discrete Mathematics

Autoren: J. Betteridge, J.H. Davenport, M.A. Freitag, W. Heijtljes, S. Kynaston, G. Sankaran, G. Traustason (2019)

Zeitschrift:
Proceedings of the 3rd Conference on Computing Education Practice, 12, 1-4

2019 | Projection methods for weak constraint variational data assimilation | M.A. Freitag, D.L.H. Green

Projection methods for weak constraint variational data assimilation

Autoren: M.A. Freitag, D.L.H. Green (2019)

2018 | GMRES convergence bounds for eigenvalue problems | M.A. Freitag, P. Kürschner, J. PestanaZeitschrift: Comput. Methods Appl. Math.Seiten: 203-222Band: 18(2)Link zur Publikation

GMRES convergence bounds for eigenvalue problems

Autoren: M.A. Freitag, P. Kürschner, J. Pestana (2018)

Zeitschrift:
Comput. Methods Appl. Math.
Seiten:
203-222
Band:
18(2)

2018 | Model reduction and approximation: theory and algorithms | M. A. FreitagZeitschrift: SIAM Rev.Seiten: 763–767Band: 60(3) (review of book)

Model reduction and approximation: theory and algorithms

Autoren: M. A. Freitag (2018)

Zeitschrift:
SIAM Rev.
Seiten:
763–767
Band:
60(3)
(review of book)

2018 | Balanced model order reduction for linear random dynamical systems driven by Lévy noise | M. Redmann, M.A. FreitagZeitschrift: To appear in J. Comput. Dyn.Link zum Preprint

Balanced model order reduction for linear random dynamical systems driven by Lévy noise

Autoren: M. Redmann, M.A. Freitag (2018)

Zeitschrift:
To appear in J. Comput. Dyn.

2018 | A low-rank approach to the solution of weak constraint variational data assimilation problems | M.A. Freitag, D.L.H. GreenZeitschrift: J. Comput. Phys.Seiten: 263-281Band: 357Link zur Publikation

A low-rank approach to the solution of weak constraint variational data assimilation problems

Autoren: M.A. Freitag, D.L.H. Green (2018)

Zeitschrift:
J. Comput. Phys.
Seiten:
263-281
Band:
357

2015 | Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration | M.A. Freitag, P. KürschnerZeitschrift: Numer. Linear Algebra Appl.Seiten: 175–196Band: 22(1)Link zur Publikation

Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration

Autoren: M.A. Freitag, P. Kürschner (2015)

Zeitschrift:
Numer. Linear Algebra Appl.
Seiten:
175–196
Band:
22(1)

2015 | The effect of numerical model error on data assimilation | S.E. Jenkins, C.J. Budd, M.A. Freitag, N.D. SmithZeitschrift: J. Comput. Appl. Math.Seiten: 567 – 588Band: 290Link zur Publikation

The effect of numerical model error on data assimilation

Autoren: S.E. Jenkins, C.J. Budd, M.A. Freitag, N.D. Smith (2015)

Zeitschrift:
J. Comput. Appl. Math.
Seiten:
567 – 588
Band:
290

2014 | A new approach for calculating the real stability radius | M.A. Freitag, A. SpenceZeitschrift: BITVerlag: SpringerSeiten: 381-400Band: 54(2)Link zur Publikation

A new approach for calculating the real stability radius

Autoren: M.A. Freitag, A. Spence (2014)

Zeitschrift:
BIT
Verlag:
Springer
Seiten:
381-400
Band:
54(2)

2014 | Calculating the $H_\infty$-norm using the implicit determinant method | M.A. Freitag, A Spence, P. Van DoorenZeitschrift: SIAM J. Matrix Anal. Appl.Seiten: 619-635Band: 35(2)Link zur Publikation

Calculating the $H_\infty$-norm using the implicit determinant method

Autoren: M.A. Freitag, A Spence, P. Van Dooren (2014)

Zeitschrift:
SIAM J. Matrix Anal. Appl.
Seiten:
619-635
Band:
35(2)

2014 | The computation of Jordan blocks in parameter-dependent matrices | R.O. Akinola, M.A. Freitag, A. SpenceZeitschrift: IMA J. Numer. Anal.Verlag: Oxford University PressSeiten: 955-976Band: 34(3)Link zur Publikation

The computation of Jordan blocks in parameter-dependent matrices

Autoren: R.O. Akinola, M.A. Freitag, A. Spence (2014)

Zeitschrift:
IMA J. Numer. Anal.
Verlag:
Oxford University Press
Seiten:
955-976
Band:
34(3)

2014 | The calculation of the distance to a nearby defective matrix | R.O. Akinola, M.A. Freitag, A. SpenceZeitschrift: Numer. Linear Algebra Appl.Seiten: 403-414Band: 21(3)Link zur Publikation

The calculation of the distance to a nearby defective matrix

Autoren: R.O. Akinola, M.A. Freitag, A. Spence (2014)

Zeitschrift:
Numer. Linear Algebra Appl.
Seiten:
403-414
Band:
21(3)

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

Large Scale Inverse Problems: Computational Methods and Applications in the Earth Sciences

Autoren: M. Cullen, M.A. Freitag, S. Kindermann and R. Scheichl (Editors) (2013)

Reihe:
Radon Series on Computational and Applied Mathematics, Vol. 13
Verlag:
De Gruyter, Berlin

2013 | Synergy of inverse problems and data assimilation techniques. Large Scale Inverse Problems | M.A. Freitag, R.W.E PotthastZeitschrift: Radon Ser. Comput. Appl. Math.Verlag: De GruyterBand: 13 (Preprint)

Synergy of inverse problems and data assimilation techniques. Large Scale Inverse Problems

Autoren: M.A. Freitag, R.W.E Potthast (2013)

Zeitschrift:
Radon Ser. Comput. Appl. Math.
Verlag:
De Gruyter
Band:
13

2013 | The Origin of Power-Law Emergent Scaling in Large Binary Networks | D.P. Almond, C.J. Budd, M.A. Freitag, G.W. Hunt, N.J. McCullen, N.D. SmithZeitschrift: Phys. ASeiten: 1004-1027Band: 392(4)Link zur Publikation , Link zum Preprint

The Origin of Power-Law Emergent Scaling in Large Binary Networks

Autoren: D.P. Almond, C.J. Budd, M.A. Freitag, G.W. Hunt, N.J. McCullen, N.D. Smith (2013)

Zeitschrift:
Phys. A
Seiten:
1004-1027
Band:
392(4)

2013 | Resolution of sharp fronts in the presence of model error in variational data assimilation | M.A. Freitag, N.K. Nichols, C.J. BuddZeitschrift: Q. J. R. Meteorol. Soc.Seiten: 742-757Band: 139Link zur Publikation

Resolution of sharp fronts in the presence of model error in variational data assimilation

Autoren: M.A. Freitag, N.K. Nichols, C.J. Budd (2013)

Zeitschrift:
Q. J. R. Meteorol. Soc.
Seiten:
742-757
Band:
139

2011 | A Newton-based method for the calculation of the distance to instability | M.A. Freitag, A. SpenceZeitschrift: Linear Alg. Appl.Seiten: 3189-3205Band: 435(12)Link zur Publikation

A Newton-based method for the calculation of the distance to instability

Autoren: M.A. Freitag, A. Spence (2011)

Zeitschrift:
Linear Alg. Appl.
Seiten:
3189-3205
Band:
435(12)

2011 | Regularization techniques for ill-posed inverse problems in data assimilation | M.A. Freitag, N.K. Nichols, C.J. BuddZeitschrift: Comput. & FluidsSeiten: 168-173Band: 46(1)Link zur Publikation

Regularization techniques for ill-posed inverse problems in data assimilation

Autoren: M.A. Freitag, N.K. Nichols, C.J. Budd (2011)

Zeitschrift:
Comput. & Fluids
Seiten:
168-173
Band:
46(1)

2010 | L1-regularisation for ill-posed problems in variational data assimilation | M.A. Freitag, N.K. Nichols, C.J. BuddZeitschrift: PAMMSeiten: 665-668Band: 10(1)Link zur Publikation

L1-regularisation for ill-posed problems in variational data assimilation

Autoren: M.A. Freitag, N.K. Nichols, C.J. Budd (2010)

Zeitschrift:
PAMM
Seiten:
665-668
Band:
10(1)

2009 | Shift-invert Arnoldi's method with preconditioned iterative solves | M.A. Freitag, A. SpenceZeitschrift: SIAM J. Matrix Anal. Appl.Seiten: 942-969Band: 31(3)Link zur Publikation

Shift-invert Arnoldi's method with preconditioned iterative solves

Autoren: M.A. Freitag, A. Spence (2009)

Zeitschrift:
SIAM J. Matrix Anal. Appl.
Seiten:
942-969
Band:
31(3)

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

The calculation of the distance to instability by the computation of a Jordan block

Autoren: M. Freitag (joint work with A. Spence) (2009)

Oberwolfach Report No. 37/2009. (Report)

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

Rayleigh quotient iteration and simplified Jacobi-Davidson with preconditioned iterative solves for generalised eigenvalue problems

Autoren: M.A. Freitag, A. Spence, E. Vainikko (2008)

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

The Impact of Multiplication Operators on the Ill-Posedness of Inverse Problems

Autoren: Melina Freitag (2008)

168 pages, VDM Verlag Dr. Müller Aktiengesellschaft & Co. KG (2008). (Available online here)

2008 | Rayleigh Quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves | M.A. Freitag, A. SpenceZeitschrift: Linear Alg. Appl.Verlag: ElsevierSeiten: 2049-2060Band: 428(8-9)Link zur Publikation

Rayleigh Quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves

Autoren: M.A. Freitag, A. Spence (2008)

Zeitschrift:
Linear Alg. Appl.
Verlag:
Elsevier
Seiten:
2049-2060
Band:
428(8-9)

2008 | A tuned preconditioner for inexact inverse iteration applied to Hermitian eigenvalue problems | M.A. Freitag, A. SpenceZeitschrift: IMA J. Numer. Anal.Verlag: Oxford University PressSeiten: 522-551Band: 28(3)Link zur Publikation

A tuned preconditioner for inexact inverse iteration applied to Hermitian eigenvalue problems

Autoren: M.A. Freitag, A. Spence (2008)

Zeitschrift:
IMA J. Numer. Anal.
Verlag:
Oxford University Press
Seiten:
522-551
Band:
28(3)

2007 | Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem | M.A. Freitag, A. SpenceZeitschrift: Electron. Trans. Numer. Anal.Seiten: 40-64Band: 28Link zum Preprint

Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem

Autoren: M.A. Freitag, A. Spence (2007)

Zeitschrift:
Electron. Trans. Numer. Anal.
Seiten:
40-64
Band:
28

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

Inner-outer Iterative Methods for Eigenvalue Problems - Convergence and Preconditioning

Autoren: M. A. Freitag (2007)

PhD Thesis, Department of Mathematical Sciences, University of Bath (2007). (Gzipped PostScript), (PDF)

2007 | The Preissmann box scheme and its modification for transcritical flows | M.A. Freitag, K. W. MortonZeitschrift: Internat. J. Numer. Methods Engrg.Verlag: WileySeiten: 791-811Band: 70(7)Link zur Publikation

The Preissmann box scheme and its modification for transcritical flows

Autoren: M.A. Freitag, K. W. Morton (2007)

Zeitschrift:
Internat. J. Numer. Methods Engrg.
Verlag:
Wiley
Seiten:
791-811
Band:
70(7)

2007 | Convergence rates for inexact inverse iteration with application to preconditioned iterative solves | M.A. Freitag, A. SpenceZeitschrift: BITVerlag: SpringerSeiten: 27-44Band: 47(1)Link zur Publikation

Convergence rates for inexact inverse iteration with application to preconditioned iterative solves

Autoren: M.A. Freitag, A. Spence (2007)

Zeitschrift:
BIT
Verlag:
Springer
Seiten:
27-44
Band:
47(1)

2005 | Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems | M. Freitag, B. HofmannZeitschrift: J. Inverse Ill-Posed Probl.Seiten: 123-148Band: 13(2)Link zur Publikation

Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems

Autoren: M. Freitag, B. Hofmann (2005)

Zeitschrift:
J. Inverse Ill-Posed Probl.
Seiten:
123-148
Band:
13(2)

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

On the Influence of Multiplication Operators on the Ill-posedness of Inverse Problems

Autoren: M. Freitag (2004)

Diplomarbeit, Fakultät für Mathematik, Technische Universität Chemnitz (2004). (Available online here)

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

Transcritical flow modelling with the Box Scheme

Autoren: M. Freitag (2003)

MSc Thesis, Department of Mathematical Sciences, University of Bath (2003). (GZipped PostScript), (PDF)

Anschrift

Universität Potsdam
Institut für Mathematik
Campus Golm, Haus 9
Karl-Liebknecht-Str. 24-25
D-14476 Potsdam

Aktivitäten

25.05.2022, 16:00  –  Campus Golm, building 9, room 0.17
SFB-Seminar

Learning in High-Dimensional Feature Spaces Using ANOVA-Based Fast Matrix-Vector Multiplication

Theresa Wagner, TU Chemnitz

Kernel matrices are crucial in many learning tasks and typically dense and large-scale. Depending on the dimension of the feature space even the compu- tation of all its entries in reasonable time... 

mehr erfahren

25.05.2022, 13:30  –  Haus 9, Raum 0.17 und Zoom
Forschungsseminar Diskrete Spektraltheorie

Laplacians on Riemann surfaces and Graphs

Noema Nicolussi (Potsdam)

There are many interesting parallels between analysis on Riemann surfaces and graphs. Both settings admit a Laplace operator and the Poisson equation reflects crucial geometric information.

Motivated... 

mehr erfahren

30.05.2022, 10:00  –  hybrid (room 2.9.2.22 and on zoom)
Forschungsseminar Statistik

Statistics at the IQTIG - Analyzing Health Care Data

Maurilio Gutzeit

We start with a short introduction to the IQTIG (Institut für Qualitätssicherung und Transparenz im Gesundheitswesen) as a key player in quality insurance in the German health care system and to the... 

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30.05.2022, 13:00  –  Golm, Haus 9 Raum 2.22
Forschungsseminar Wahrscheinlichkeitstheorie

Random Dynamics in Collective Behaviour - Consensus, Clustering and Extinction of Populations

Jens Fischer (Toulouse, UP)

Social network models are a common tool to further the understanding of relation based interactions in societies. Nonetheless, a complete mathematical understanding is lacking due to the complexity of... 

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31.05.2022, 12:30  –  Golm, Haus 9, Raum 2.22
Forschungsseminar Wahrscheinlichkeitstheorie

Percolation of the level set of the Gaussian Free Field on a Galton-Watson tree.

Gioele Gallo (Köln)

The study of Gaussian free field level sets on supercritical Galton-Watson trees has been initiated by Abächerli and Sznitman. We continue this investigation by means of different tools in order to... 

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