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Unit M15: Applied Numerical Analysis

Technische Universität München
Fakultät für Mathematik
Boltzmannstr. 3
85748 Garching bei München
Secretary
Silvia Toth-Pinter
Tel.: +49 (0) 89 289 18434
e-mail: Toth-Pinterematma.tum.de

LogoM15

Our vision The dimension scale of problems arising in our modern information society became very large. A new area of science and engineering is now urgently needed in order to extract and interpret significant information from the universe of data collected from a variety of modern sources (Internet, physics experiments, medical diagnostics, etc.). Numerical simulations at the required scale will be one of the great challenges of the 21st century. In short, we need to become capable of organizing and understanding complexity.

Compression and dimensionality reduction The most notable recent advances in data analysis and numerical simulation are based on the observation that in several situations, even for very complex phenomena, only a few governing components are required to describe the whole dynamics; a dimensionality reduction can be achieved by demanding that the solution be "sparse" or "compressible". Since the relevant degrees of freedom are not prescribed, and may depend on the particular solution, we need efficient optimization methods for solving the hard combinatorial problem of identifying them.

Our research In the Unit M15 -- Applied Numerical Analysis we are first addressing the problem of designing efficient algorithms which allow us to achieve sparse optimization in high-dimensions. Secondly, the tools which we develop for achieving adaptive dimensionality reductions are subsequently used as building blocks for solving large-scale partial differential equations or variational problems arising in various contexts. Finally, we are applying the whole machinery to interesting applications in image processing, numerical simulation, and we are exploring new applications in innovative fields such as automatic learning of dynamical systems.


News

2016
July 18–22, 2016 Felix Krahmer is organizing a Summer School about Mathematical methods for high-dimensional data analysis together with Ulrich Bauer Pfeil, ISAM und TopMath and SFB/TR 109 Pfeil. Please register until May 15!
July 15–30, 2016 Peter Massopust was awarded a GIAN lectureship under the GIAN initiative (Global Initiative of Academic Networks Pfeil) and will hold a two-week long lecture series on "Splines and Fractals in Approximation and Interpolation Theory" at IIT Madras, India.
   
May 1, 2016 Sandro Belz and Michael Sandbichler start their work at our research unit.
April 19, 2016 Peter Massopust, Brigitte Forster, and Ole Christensen have completed the paper ''Fractional and Complex Pseudo-Splines and the Construction of Parseval Frames.'' [ .pdf ]
Feb. 29 - Mar. 04, 2016 Peter Massopust attended the international IM-Workshop on Applied Approximation, Signals and Images Pfeil in Bernried, Germany, and gave a presentation on "Fractional and Complex Pseudo-Splines.
Feb. 15, 2016 Peter Massopust completed the second edition of his research monograph ''Fractal Functions, Fractal Surfaces, and Wavelets.'' It will be published by Elsevier later this year.
Feb. 12, 2016 We are organizing the Second Workshop Donau-Isar-Inn: WDI² - Approximation Theory and Applications. We invite researchers, PhD students and other students to join us to learn about current topics in the mathematics of signal processing, applied harmonic analysis and approximation theory. Update: Talk titles and abstracts available now.
Feb. 1 - 12, 2016 Dr. Jeff Hogan Pfeil (University of Newcastle, Australia) will visit Peter Massopust to extend and strengthen their collaboration on the applicability of Clifford-analytical methods to multi-channel signal and image processing.
Feb. 1, 2016 Young-Pil Choi Pfeil starts his work at our research unit.
Jan. 11, 2016 Dominik Stöger starts his work at our research unit.
Jan. 1, 2016 Sara Krause-Solberg, Johannes Maly, and PD Dr. Peter Massopust start their work at our research unit.
2015
Oct. 31, 2015 Giacomo Albi, Lorenzo Pareschi and Mattia Zanella concluded the paper ''On the optimal control of opinion dynamics on evolving networks''. [ .pdf ]
Oct. 1, 2015 Christian Kümmerle starts his work at our research unit.
Sep. 14, 2015 Massimo Fornasier, Steffen Peter, Holger Rauhut, and Stephan Worm concluded the paper "Conjugate gradient acceleration of iteratively re-weighted least squares methods" [ .pdf ]
Aug. 25, 2015 Giacomo Albi, Marco Artina, Massimo Fornasier and Peter Markowich concluded the paper ''Biological Transportation Networks: Modeling and Simulation''. [ .pdf ]
July 29 2015 We are inviting interested candidates to apply for 1 Doctoral position within the project "Quantization and Noise Robustness in Distributed Compressed Sensing"(led by Prof. Massimo Fornasier) at the Technical University of Munich NEW APPLICATION DEADLINE OCTOBER 31, 2015 [ details ]
July 15, 2015 Joe-Mei Feng starts her work at our research unit.
June 28, 2015 Massimo Fornasier and Steffen Peter concluded the book chapter "An Overview on Algorithms for Sparse Recovery" for the book "Sparse Reconstruction and Compressive Sensing in Remote Sensing", edited by X. Zhu and R. Bamler [ .pdf ]
Apr. 26, 2015 Juliane Sigl concluded the paper "Nonlinear Residual Minimization by Iteratively Reweighted Least Squares" [ .pdf ]
Apr. 16, 2015 Giacomo Albi, Mattia Bongini, Emiliano Cristiani and Dante Kalise concluded the paper "Invisible control of self-organizing agents leaving unknown environments" [ .pdf ]
Apr. 9, 2015 We are inviting interested candidates to apply within the context of the Emmy Noether Junior Research Group "Randomized Sensing and Quantization of Signals and Images" (led by Prof. Felix Krahmer) at the Technical University of Munich details
Apr. 1, 2015 Felix Krahmer starts his work at our research unit.
Mar. 3, 2015 Giacomo Albi, Lorenzo Pareschi and Mattia Zanella concluded the paper "Uncertainty Quantification in Control Problems for Flocking Models" [ .pdf ]
Feb. 12, 2015 In this important day of negotiations in Minsk, Massimo Fornasier expresses with great preoccupation strong moral support to the strenuous attempts to bring peace to Ukraine and to stop a potential disaster for the entire Europe
Jan. 1, 2015 We announce that Professor Peter Markowich Pfeil will be visiting our department as a John Von Neumann Professor in the period January-March 2015. He will deliver the special lecture On some (modern) Problems in Applied Differential Equations.
2014
Aug. 25, 2014 Mattia Bongini, Massimo Fornasier, Oliver Junge, and Benjamin Scharf concluded the paper "Sparse Control of Alignment Models in High Dimension" [ .pdf ]
Aug. 19, 2014 Stephan Dahlke, Lars Diening, Christoph Hartmann, Benjamin Scharf, and Markus Weimar concluded the paper "Besov regularity of solutions to the p-Poisson equation" [ .pdf ]
July 15, 2014 Giacomo Albi, Lorenzo Pareschi and Mattia Zanella concluded the paper "Boltzmann type control of opinion consensus through leaders" [ .pdf ]
June 30, 2014 Benjamin Scharf was awarded the "Promotionspreis der Fakultät für Mathematik und Informatik der FSU Jena" for his PhD-Thesis.
May 26, 2014 Marco Artina, Massimo Fornasier, Stefano Micheletti, and Simona Perotto concluded the paper "Anisotropic mesh adaptation for crack detection in brittle materials" [ .pdf ]
May 23, 2014 Marco Artina, Massimo Fornasier, Stefano Micheletti, and Simona Perotto concluded the paper "The benefits of anisotropic mesh adaptation for brittle fractures under plane-strain condition" [ .pdf ]
May 11, 2014 Giacomo Albi was awarded the Nicolò Copernico Prize Pfeil prize for his PhD thesis.
May 1, 2014 Giacomo Albi starts his work at our research unit.
May 1, 2014 We announce that Professor Mauro Maggioni Pfeil will be visiting our department as a John Von Neumann Professor in the period May-July 2014. He will deliver the special lecture Statistical Learning, Geometry and High-Dimensional Probability .
April 30, 2014 Mattia Bongini, Massimo Fornasier, and Dante Kalise concluded the paper "(Un)conditional consensus emergence under perturbed and decentralized feedback controls" [ .pdf ]
Mar. 26, 2014 Valeriya Naumova and Steffen Peter concluded the paper with title "Minimization of multi-penalty functionals by alternating iterative thresholding and optimal parameter choices". [ .pdf ]
Feb. 7, 2014 Mattia Bongini, Agata Ciabattoni and Franco Montagna concluded the paper "Proof Search and Co-NP Completeness for Many-Valued Logics"
Feb. 3, 2014 Markus Hansen starts his work at our research unit.
Jan. 22, 2014 We offer 2 new Master-thesis. link
Jan. 16, 2014 Marco Artina, Massimo Fornasier, and Steffen Peter updated the paper "Damping Noise-Folding and Enhanced Support Recovery in Compressed Sensing". [ .pdf ]
2013
Nov. 15, 2013 Marco Artina, Massimo Fornasier, Stefano Micheletti, and Simona Perotto concluded the ENUMATH conference proceeding "Anisotropic adaptive meshes for brittle fractures: parameter sensitivity" [ .pdf ]
Oct. 22, 2013 We announce that Professor Götz Pfander Pfeil will be visiting our department as a John Von Neumann Professor in the period January-June 2014. He will deliver the special lecture Time-Frequency Analysis and Applications in Information Theory.
Sept. 27, 2013 Michael Speckbacher concluded his Master Thesis with the title "Time-frequency representation adapted to perception". [ .pdf ]
Sept. 25, 2013 Martin Eller participated in the Studierendenkonferenz of Österreichische Mathematische Gesellschaft and Deutsche Mathematiker-Vereinigung 2013 and gave a talk on his Master thesis "Rotation Invariance in Exemplar-based Image Inpainting". His contribution was awarded with a main price.
Sept. 11, 2013 Mattia Bongini and Massimo Fornasier concluded the paper with title "Sparse Stabilization of Dynamical Systems Driven by Attraction and Avoidance Forces". [ .pdf ]
Sept. 1, 2013 Martin Eller concluded his Master Thesis with the title "Rotation Invariance in Exemplar-based Image Inpainting". [ .pdf ]
Jul. 23, 2013 Massimo Fornasier, Valeriya Naumova, and Sergei Pereverzyev concluded the paper with title "Parameter Choice Strategies for Mult-Penalty Regularization". [ .pdf ]
Jul. 15, 2013 Martin Ehler Pfeil, Massimo Fornasier, and Juliane Sigl concluded the paper with title "Quasi-linear compressed sensing". [ .pdf ]
Jul. 10, 2013 Massimo Fornasier and Francesco Solombrino concluded the paper with title "Mean-field optimal control". [ .pdf ]
Jun. 15, 2013 Benjamin Scharf concluded the paper with title "Wavelet decomposition techniques and Hardy inequalities for function spaces on cellular domains". [ .pdf ]
May 31, 2013 Jan-Christian Hütter concluded his Master Thesis with the title "Minimizers and Gradient Flows of Attraction-Repulsion Functionals with Power Kernels and Their Total Variation Regularization". [ .pdf ]
Mar. 31, 2013 Juliane Sigl concluded her Master Thesis with the title "Quasilinear compressed sensing". [ .pdf ]
Mar. 25, 2013 We concluded the paper "Damping Noise-Folding and Enhanced Support Recovery in Compressed Sensing". [ .pdf ]
Mar. 21, 2013 Tenure Track Assistant Professorship »Optimization and Data Analysis« with deadline for applications April 30, 2013.
Mar. 15, 2013 Marco Artina and Steffen Peter are invited to give talks in the Minisymposia "Adaptive finite elements" and "Approximation, compression, and data analysis" at ENUMATH 2013 Pfeil, Lausanne August 26-30, 2013
Mar. 15, 2013 Massimo Fornasier is co-organizing (with Philipp Grohs Pfeil and Rachel Ward Pfeil) the Minisymposium "Approximation, compression, and data analysis" at ENUMATH 2013 Pfeil, Lausanne August 26-30, 2013
Mar. 1, 2013 Benjamin Scharf starts his work at our research unit working on Besov regularity and High Dimensional Sparse Optimal Control
Jan. 31, 2013 Mattia Bongini, Massimo Fornasier, Fabian Fröhlich and Laleh Hagverdi concluded the paper "Sparse control of force field dynamics" [ .pdf ]
Jan. 1, 2013 Mattia Bongini starts his work at our research unit working on High Dimensional Sparse Optimal Control
2012
Dec. 7, 2012 Martin Eller starts his work at our research unit working on Variational Exemplar-Based Image Inpainting
Oct. 21, 2012 We concluded a paper on the mathematics of consensus control [ .pdf ]
Sept. 1, 2012 Marco Artina starts his work at our research unit working on Lagrangian methods for constrained nonconvex minimization
Aug. 8 - Sept. 8, 2012 OUT OF OFFICE -- checking emails but slowly responding!!!
Aug. 10, 2012 Massimo Fornasier has been invited to be a Member of the Institute for Advanced Studies Pfeil at the Technical University of Munich (IAS-TUM)
July 19, 2012 2 Postdoc and 1 Doc positions: we are inviting interested candidates to apply within the ERC-Starting Grant project "High-Dimensional Sparse Optimal Control" at the Technical University of Munich details -- Deadline for applications: September 30, 2012
July 19, 2012 Massimo Fornasier has been awarded an ERC-Starting Grant for the project High-Dimensional Sparse Optimal Control
July 4, 2012 Inaugural lecture of Massimo Fornasier at Technische Universität München, topic: Random Dimensionality Reduction and Sparse Recovery Algorithms, 17:00, Hörsaal 3, abstract: pdf
June 1, 2012 Jan-Christian Hütter starts his work at our research unit working on gradient flow of repulsion and attraction potentials
May 22, 2012 The START Project "Sparse Approximation and Optimization in High Dimensions" link Pfeil has been prolonged for further 3 years
May 22, 2012 Massimo Fornasier is invited to deliver a "Lezione Lagrangiana" at the Department of Mathematics of the University of Torino official announcement
May 14, 2012 Karin Schnass Pfeil has successfully obtained an FWF Erwin-Schrödinger-Fellowship to be spent at the University of Sassari (Italy)
May 2, 2012 Juliane Sigl starts her work at our research unit working on compressed sensing techniques for pulsating stars
April 2, 2012 Steffen Peter starts his work at our research unit working on compressed sensing techniques in remote sensing and Earth observation
2011
December 24, 2011 Massimo Fornasier was awarded the Biennial SIMAI Prize Pfeil by the Società Italiana di Matematica Applicata ed Industriale
October 18, 2011 Article "Mathematiker setzt lückenhaftes Mega-Puzzle zusammen" by Holger Dambeck on "Spiegel On Line" link Pfeil
April 1, 2011 new chair Applied Numerical Analysis, starting with the activity of Massimo Fornasier as Professor at the Technical University of Munich

-- SteffenPeter - 17 Apr 2012