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In der laufenden Saison 2023/24 meldet der SV Deuchelried...
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Am 13. und 14. Januar richtet die Tischtennisabteilung des...
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29. Jan. 2021 · We propose a `tensor-train singular value decomposition' (TT-SVD) algorithm based on two building blocks: a `Q-less tall-skinny QR' factorization, and a fused tall-skinny matrix-matrix multiplication and reshape operation.
- Melven Röhrig-Zöllner, Jonas Thies, Achim Basermann
- G.4; G.1.3
- 2021
- 26 pages, 16 figures, accepted by SISC
- Randomized SVD For Matrices
- Listing 1 Randomized Range Approximation
- Theorem 1
- Randomized Tt-Svd
- Listing 2 Randomized Tt-Svd
- Theorem 2
- Proof
- Proposition 1
Randomized techniques for the calculation of SVD or QR factorizations of matrices have been proposed many times in the literature. However it was only recently that, thanks to the application of new results from random matrix theory, these procedures could be analyzed rigorously. We start this section by presenting some results from the work of Hal...
Input : ∖(∖ mathbf A,∖ r ,∖ p∖) Output : ∖(∖ mathbf Q∖) Create a standard Gaussian random matrix ∖(∖ mathbf{ G } ∖ in ∖mathbb{ R}ˆ{n_2 ∖times ( r+ p)}∖) Calculate the intermediate matrix ∖(∖ mathbf B := ∖mathbf{ A } ∖mathbf{ G } ∖ in ∖mathbb{ R}ˆ{n_1 ∖times s }∖). Compute the factorization ∖(∖ mathbf Q ∖mathbf R = ∖mathbf B∖). The following theorem...
Given \(\mathbf A \in \mathbb {R}^{m \times n}\) and s =r +p with p ≥ 2. For the projection Q obtained by procedure 1, there holds the following error bounds. with probability at least 1 − 6p−p and for p ≥ 4 and any u, t ≥ 1 with probability at least \(1 - 5t^{-p}-2e^{-u^2/2}\). Let us highlight furthermore that for the operator norm, we have that ...
In this section we show how the same idea of the randomized range approximation for matrices can be used to formulate a randomized algorithm that calculates an approximate TT-SVD of arbitrary tensors. We show that stochastic error bounds analogous to the matrix case can be obtained. Furthermore we show that for sparse tensors, this randomized TT-SV...
Input : ∖(∖ mathbf x∖) , Output : ∖(∖ mathbf W_1, ∖ ldots , ∖mathbf W_d∖) Set ∖(∖ mathbf b_{d+1} := ∖mathbf x∖) For ∖( j= d , ∖ ldots , 2∖): Create a Gaussian random tensor ∖(∖ mathbf g ∖ in ∖mathbb{ R}ˆ{ s_{j −1} ∖ times n_1 ∖ times ∖ ldots ∖ times n_ { j −1}}∖) Calculate ∖(∖ mathbf a_{ j } := ∖mathbf g ∖ circ_ {(2 , ∖ ldots j ) , (1 , ∖ ldots , j...
Given \(\mathbf x \in \mathbb {R}^{n_1 \times \ldots \times n_d}\), s =r +p with p ≥ 4. For every u, t ≥ 1, the error of the randomized TT-SVD, as given in Listing 2, fulfills with probability at least \((1 - 5t^{-p}-2e^{-u^2/2})^{d-1}\) . The parameter η is given as
For syntactical convenience let us define \(\mathbf B_i := \left ( \hat M_{\{1, \ldots , i-1\}} ( \mathbf b_i ) \right )T\). Then as \(\hat P_{2,\ldots ,d}\)is an orthogonal projector, we have For all 2 ≤ i ≤ d, there holds where we used that \(\mathbf Q_iT \mathbf Q_i\) is an orthogonal projector as well. Inserting this iteratively into (46) gives...
Assume that \(\mathbf x \in \mathbb {R}^{n_1 \times \ldots \times n_d}\) contains at most N non-zero entries. Then the computational complexity of the randomized TT-SVD given in Listing 2 scales as \(\mathcal {O}(d(s^2 N +s^3 n))\).
- Benjamin Huber, Reinhold Schneider, Sebastian Wolf
- 2017
In der laufenden Saison 2023/24 meldet der SV Deuchelried insgesamt 19 Mannschaften bei den Damen, Herren, Mädchen und Jungen. Eine Übersicht über alle Mannschaften findet sich hier.
13. Jan. 2024 · Am 13. und 14. Januar richtet die Tischtennisabteilung des SV Deuchelried die Baden-Württembergischen Einzelmeisterschaften der Seniorinnen und Senioren in Wangen im Allgäu aus. NEU: *** Informationen zum Turnier *** Auslosung *** Zeitplan ***. Hier geht es zu der Ausschreibung. Download Meldeformular.
13. Nov. 2021 · After optimizing the batched core tensor, we can recover the two original core tensors by using singular value decomposition (SVD), which enables us to modify the TT ranks by truncating the SVD result.
Tensor Train Singular Value Decomposition (TT-SVD) The intuition of the TT-SVD is that in every step, a (matrix) SVD is performed to detach one open mode from the tensor. Figure 2 shows this process step-by-step for an order four tensor and is frequently referred to in the following description.
