Optimized Tensor-Product Approximation Spaces
By Michael Griebel, Stephan Knapek. 2000
137 citations recorded by the source corpus.
Subfields: Computational Mechanics, Computer Vision and Pattern Recognition
View Paper: https://www.semanticscholar.org/paper/fb59b2f82f1518d41e3ea330f795291df1477cea
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
- Boris N. Khoromskij
- Ivan P. Gavrilyuk
- Christoph Schwab
- Reinhold Schneider
- Michael Griebel
- Heinz-Jürgen Flad
- Wolfgang Hackbusch
- Markus Bachmayr
In Computer Vision and Pattern Recognition
- Boris N. Khoromskij
- Ivan P. Gavrilyuk
- Wolfgang Hackbusch
- Michael Griebel
- Reinhold Schneider
- Heinz-Jürgen Flad
- Christoph Schwab
- Markus Bachmayr
Citations in the corpus
- Adaptive wavelet methods for solving operator equations: An overview (2009, unknown): “as optimized sparse-grid spaces ([GK00]).”
- Concepts of Data-Sparse Tensor-Product Approximation in Many-Particle Modelling (2008, methodology): “We refer to [49, 80] and references therein for the detailed exposition of this approach.”
- NUMERICAL SOLUTION OF PARABOLIC EQUATIONS IN HIGH DIMENSIONS (2004, background): “It was shown in [4] for p = 1 that one can avoid this logarithmic term by using smaller spaces than V̂ L and higher regularity of u than H.”
- Hierarchical Tensor-Product Approximation to the Inverse and Related Operators for High-Dimensional Elliptic Problems (2005, background): “[25], [13]) allows to get rid of this phenomenon.”
- Adaptive low rank wavelet methods and applications to two-electron Schrödinger equations (2012, background): “Proofs are given in [154], see also [68, 44] for the case of bounded domains.”
- Hyperbolic Cross Approximation (2016, methodology): “These studies have been continued in Griebel, Knapek [154, 155], Bungartz, Griebel [47], Griebel [153], Schwab, Süli, Todor [297], and Dinh Dũng, Ullrich [110].”
- Dimension–Adaptive Tensor–Product Quadrature (2003, background): “as a binary knapsack problem [5, 15], which is closely related to best N–term approximation [8].”
- Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part II. HKT Representation of Certain Operators (2005, background): “Alternative ideas based on sparse grid finite elements/wavelets have been successfully applied [3], [18], [12], [19].”