profile picture   Dr. Sebastian Krämer

Institut für Geometrie und Praktische Mathematik
RWTH Aachen
Templergraben 55
52056 Aachen
Germany

research group:
Prof. Lars Grasedyck
office:
Hauptgebäude 104.2
phone:
+49 241 80-94875
email:
kraemer@igpm.rwth-aachen.de


Preprints

[2] Asymptotic log-det sum-of-ranks minimization via tensor (alternating) iteratively reweighted least squares.
S. Krämer, arXiv:2106.15201 (2021)
[arXiv]
[1] Asymptotic log-det rank minimization via (alternating) iteratively reweighted least squares.
S. Krämer, arXiv:2106.14644 (2021)
[arXiv]

Publications

[3] A geometric description of feasible singular values in the tensor train format.
S. Krämer, SIAM Journal on Matrix Analysis and Applications, 40, pp. 1153-1178 (2019)
[epubs.siam]
[2] Stable ALS approximation in the TT-format for rank-adaptive tensor completion.
L. Grasedyck and S. Krämer, Numer. Math. 143, 855–904 (2019)
[springer link]
[1] Variants of alternating least squares tensor completion in the tensor train format.
L. Grasedyck, M. Kluge, and S. Krämer, SIAM Journal on Scientific Computing 37, pp. A2424-A2450 (2015)
[epubs.siam]

PhD Thesis

Tree tensor networks, associated singular values and high-dimensional approximation.
S. Krämer, RWTH Aachen University (2020)
[publications.rwth-aachen]

Talks (little excerpt)

[i_4] Guaranteed and fast construction of tensors with prescribed largest multilinear singular values.
Online Minisymposium on Low-rank Geometry and Computation, organized by MPI, Leipzig, Germany (2020)
[online]
[i_3] Approximate interpolation of high dimensional, scattered data in tree tensor formats.
Algorithms and Applications of High Dimensional Approximation, Bath, England (2019)
[Bath]
[i_2] Feasible singular values for hierarchical tensors.
Algebraic Geometry, Approximation, and Optimisation, Creswick, Australia (2018)
[Crezwick]
[i_1] Stable ALS Approximation for Rank-Adaptive Tensor Completion.
GAMM Jahrestagung, Munich, Germany (2018)
[Munich]

Repositories

paths network (A)IRLS Library
Matlab implementations of (alternating) IRLS algorithms for affine vector cardinality, matrix rank and tensor sum-of-rank minimization.
[Git Repository]
button plot Button Plot
Custom plot function that iteratively combines clusters of visually intersecting disks in a scatter plot avoiding quadratic complexity.
[Mathworks File Exchange]
tensor node network Tensor Node Toolbox (beta version)
Toolbox for labeled, automatized tensor network arithmetic.
[Git Repository] [Live Script Walkthrough]
hive TT Feasibility Mini-Toolbox
Mini-toolbox for "A Geometrical Description of Feasible Singular Values in the Tensor Train Format"
[Git Repository] [Live Script Walkthrough]
g2s3 G2S3 (2017) Updated Course Material: Low Rank Tensor Formats
Updated exercises for the 2017 Gen Golub Summer School on Data Sparse Approximations and Algorithms for the course Low Rank Tensor Formats.
[Git Repository]
sing spec SALSA Implementation
Implementation of SALSA for "Stable ALS Approximation in the TT-Format for Rank-Adaptive Tensor Completion"
[Git Repository] [Singular Value Plot]
Code Golf Art: Savanna
Runs in Matlab command window (modified submission to the Matlab Central 20th Anniversary Minihack Contest)

figure;X=-10:.02:10;colormap([pink.*autumn;1,1,.9]);image(782./abs(X+1i*X'-3i));
hold;U=@(p)p+.5i*diff(p)*[4;0;4;4-1i+1i^cos(431*norm(p))^.5];
t=@(S,C)C{(abs(diff(S))<.01)+1}(U(S),C);f=@(P,C)[P(2);t(P(3:4),C);t(P(4:5),C);P(6)];
E=42*f(U(0:1),{f,@(P,C)[]});I=790-E/1i;fill(E+520,I,0);h=scatter(E+520,I,50,-14*abs(E));
alpha(h,.1);camva(3);


Teaching Activities

[SS21] Numerische Mathematik II (for mathematicians), two times substitutional lecturer, assistant
[WS1920 / WS2021] Numerische Mathematik I (for mathematicians), assistant
[WS1819 / SS19 / SS20 / WS2122] Mathematik I/II (for civil engineers), assistant
[SS18] Begleitpraktikum II (for mathematicians), assistant
[2017] Gene Golub Summer School on Data Sparse Approximations and Algorithms (SIAM), assistant and creator of course material
[WS1617 / WS1718] Numerische Mathematik IV (for mathematicians), assistant
[SS17] Numerische Mathematik (for electrical engineers), assistant
[SS16 / WS2122] Seminar "Aktuelle Themen der Numerik" (for mathematicians) / Numerische Multilineare Algebra (for mathematicians), assistant
[WS1415 / SS15 / WS1516] Numerische Mathematik I-III (for mathematicians), assistant
[Several years during studies] Begleitpraktikum I / II (for mathematicians), student assistant / examiner

Other

[since 2017] GAMM membership and regular participation in yearly conference
[since 2015] Review activity for SIAM