One way, how to speed up the computation of the singular value decomposition of a given matrix A ∈ C, m ≥ n, by the parallel two-sided block-Jacobi method, consists of applying some pre-processing steps that would concentrate the Frobenius norm near the diagonal. Such a concentration should hopefully lead to fewer outer parallel iteration steps needed for the convergence of the entire algorithm...

A Jacobi-type updating algorithm for the SVD or URV decomposition is developed, which is related to the QR algorithm for the symmetric eigenvalue problem. The algorithm employs one-sided transformations, and therefore provides a cheap alternative to earlier developed updating algorithms based on two-sided transformations. The present algorithm as well as the corresponding systolic implementatio...

We present high performance implementations of the QR and the singular value decomposition of a batch of small matrices hosted on the GPU with applications in the compression of hierarchical matrices. The one-sided Jacobi algorithm is used for its simplicity and inherent parallelism as a building block for the SVD of low rank blocks using randomized methods. We implement multiple kernels based ...

The Singular Value Decomposition (SVD) is an important matrix factorization with applications in signal processing, image processing and robotics. This thesis presents some of the issues involved in the design of an array of special-purpose processors connected in a mesh, for fast real time computation of the SVD. The systolic array implements the Jacobi method for the SVD. This involves plane ...

In this paper, the issue of the efficient use of Givens rotations in SVD-based QR Jacobi-type subspace tracking algorithms is addressed. By relaxing the constraint of upper triangularity on the singular value matrix, we show how even fewer Givens rotations can achieve a better diagonalization and provide more accurate singular values. Then, we investigate the efficient use of Givens rotations a...

our aim in this paper is to prove an analog of younis's theorem on the image under the jacobi transform of a class functions satisfying a generalized dini-lipschitz condition in the space $mathrm{l}_{(alpha,beta)}^{p}(mathbb{r}^{+})$, $(1< pleq 2)$. it is a version of titchmarsh's theorem on the description of the image under the fourier transform of a class of functions satisfying the dini-lip...

In this paper, the issue of the eecient use of Givens rotations in SVD-based QR Jacobi-type subspace tracking algorithms is adressed. By relaxing the constraint of upper-triangularity on the singular value matrix, we show how even fewer Givens rotations can achieve a better diagonalization and provide more accurate singular values. Then, we investigate the eecient use of Givens rotations as a v...