Alexander Litvinenko - Courses

 

Alexander Litvinenko  

 

​​        Research Themes    Projects    Teaching     Talks  


To Bachelor/Master students:  Please contact me if you like these research areas:
  1. Cheap and fast approximation of large covariance matrices. We will apply Hierarchical Matrices  (www.hlib.org, www.h2lib.org, www.hlibpro.com) to approximate huge covariance matrices (as well as the inverse, determinant, trace, square root) and reduce the computational cost.
  2. Cheap and fast approximation of covariance matrices and probability characteristic functions in high-dimensional space. We will apply  low-rank tensor methods (for instance TT toolbox from Ivan Oseledets or Hierarchical Tucker Toolbox from EPFL) to high-dimensional functions.
  3. Implement some very efficient linear algebra procedures (for instance, hierarchical matrix inverse) as a R or Matlab module.
  4. Parameter identification via maximization of the likelihood function. We will develop a low-rank surrogate of the log-likelihood function and maximize it.


To PhD students:  Please contact me if you like these research areas:

  1. Noise and uncertainty reduction in pictures obtained from electron microscopes. We will develop statistic and uncertainty quantification methods to reduce random noise and quantify uncertainty with the goal to improve the quality of microscope pictures.
  2. Decision making and risk assessment under uncertainty. We will combine uncertainty quantification techniques and decision making techniques (for instance, decision trees) for better prediction and more accurate risk estimation.
  3. Recommendation system for students and faculty members. We will develop a recommendation system which will recommend students to faculty members and vice versa.
  4. Solving parabolic PDEs with uncertain coefficients. We will develop new numerical methods, which balance the time discretisation error, hierarchical matrix approximation error, and present uncertainties.
  5. Solving hyperbolic PDEs with uncertain coefficients (you may see works of Mohammad Motamed, Fabio Nobile and Raul Tempone).

  

Teaching experience (many clickable links!):     


​2013 2014: Two mini-courses at KAUST : 

1. Low-rank tensor approximation (10 hours) (.pdf, .pdf)

2. Hierarchical Matrices (10 hours) (.pdf, .pdf​)

Lecture courses (assistant) and practical exercises at TU Braunschweig, Germany (the information is contained in Annual reports here)

2012 - 2013: Uncertainty Quantification and model reduction 

2008 2011: Introduction to Scientific Computing (~Ordinary differential equations I) 

2008 2010: Advanced Methods for ODEs and DAEs  

2010 - 2012: Introduction to PDEs and Numerical Methods  

2011 2012: Numerical simulations in fluid dynamics  

You can find this information here:  



Supervision of students:         


During 2007-2013 I supervised bachelor and master students at TU Braunschweig. Nathalie Rauschmayr sucessfully defended her Master Thesises "Coprocessing und Postprocessing von Fluidproblemen mit Paraview". Jeremy Rodriguez, Aidin Nojavan, Ates Burak, Borzoo Maiefatzade , K. Jamadar were my research assistants during 1-2 years in different projects (MUNA, CODECS).

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