We propose a new method for finding a parallel ordering needed in the parallel two-sided block-Jacobi EVD/SVD method. For a given matrix A, partitioned into block columns and block rows, such an ordering defines the subproblems that are solved in parallel in each parallel iteration step. Our approach is based on modeling the matrix block partition as a complete, edge-weighted graph, where the w...

This paper presents a new algorithm for computing the singular value decomposition (SVD) on multilevel memory hierarchy architectures. This algorithm is based on one-sided JRS iteration, which enables the computation of all Jacobi rotations of a sweep in parallel. One key point of our proposed block JRS algorithm is reusing the loaded data into cache memory by performing computations on matrix ...

We present a hierarchically blocked one-sided Jacobi algorithm for the singular value decomposition (SVD), targeting both single and multiple graphics processing units (GPUs). The blocking structure reflects the levels of GPU’s memory hierarchy. The algorithm may outperform MAGMA’s dgesvd, while retaining high relative accuracy. To this end, we developed a family of parallel pivot strategies on...

In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.

An efficient version of the parallel two-sided block-Jacobi algorithm for the singular value decomposition of an m × n matrix A includes the pre-processing step, which consists of the QR factorization of A with column pivoting followed by the optional LQ factorization of the Rfactor. Then the iterative two-sided block-Jacobi algorithm is applied in parallel to the R-factor (or L-factor). Having...

Indexing terms : Parallel algorithms, systolic arrays, matrix computation Jacobi-type matrix algorithms are mostly implemented on orthogonally connected processor arrays. In this letter, an alternative partitioning is described, resulting in a grid of hexagonally connected processors. This partitioning is shown to be over four times more efficient, as compared to the original configuration. Int...

The computation of a singular value decomposition of an m× n matrix A is certainly one of the most often demanded tasks in various applications. There are many algorithms for computing the full or partial singular value decomposition. Among them, the one-sided Jacobi method (coupled with some orderings) is reputable for its ability to compute the singular values as well as left and right singul...

formulae expressing explicitly the coefficients of an expansion of double jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. extension to expansion of triple jacobi polynomials is given. the results for the special cases of double and triple ultraspher...

Recently, the NLMeans filter has been proposed by Buades et al. for the suppression of white Gaussian noise. This filter exploits the repetitive character of structures in an image, unlike conventional denoising algorithms, which typically operate in a local neighbourhood. Even though the method is quite intuitive and potentially very powerful, the PSNR and visual results are somewhat inferior ...