This report is devoted to the proof of the global convergence and asymptotic quadratic convergence of the serial and parallel two-sided block-Jacobi SVD algorithm. In the serial case, one pair of the off-diagonal blocks with the largest weight given as the sum of squares of Frobenius norms is annihilated. In the parallel case, using the greedy implementation of dynamic ordering and having p pro...

We have designed, implemented and tested (by simulation on a serial computer) the new dynamic ordering for the parallel one-sided block-Jacobi SVD algorithm. Our idea is based on the estimation of the cosines of principal angles between two block columns X and Y of the same width without explicitly forming the matrix product XY (or Y X) and computing its SVD. Instead, we propose to use a fixed ...

We consider the problem of recovering a function f when we receive a blurred (by a linear operator) and noisy version: Yε = Kf + εẆ . We will have as guides 2 famous examples of such inverse problems: the deconvolution and the Wicksell problem. The direct problem (K is the identity) isolates the denoising operation. It cannot be solved unless accepting to estimate a smoothed version of f : for ...

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...

Graphs have so many applications in real world problems. When we deal with huge volume of data, analyzing data is difficult or sometimes impossible. In big data problems, clustering data is a useful tool for data analysis. Singular value decomposition(SVD) is one of the best algorithms for clustering graph but we do not have any choice to select the number of clusters and the number of members ...

white matter lesions (wmls) are commonly observed in strokepatients with small vessel disease (svd) and are thought toresult from a progressive, irreversible disease process followingarteriolosclerosis. in this study, we report a case of partialdisappearance of wmls 1 year after a lacunar stroke in a69-year-old man with evidence of svd. we also discuss possiblemechanisms associated with this ob...

Swine vesicular disease (SVD) is a highly contagious viral disease that causes vesicular disease in pigs. The importance of the disease is due to its indistinguishable clinical signs from those of foot-and-mouth disease, which prevents international trade of swine and related products. SVD-specific antibody detection via an enzyme-linked immunosorbent assay (ELISA) is the most versatile and com...

Cerebral small vessel disease (SVD) is an important cause of vascular cognitive impairment. Recent studies have demonstrated that structural connectivity of brain networks in SVD is disrupted. However, little is known about the extent and location of the reduced connectivity in SVD. Here they investigate the rich club organisation-a set of highly connected and interconnected regions-and investi...

Identifiability, observability, and controllability are important structural properties of a dynamic system model. Our interest lies in the detection lack identifiabil-ity/observability and/or through computation subsequent analysis exact nullspace gramian for non-linear systems. For this we have developed user-friendly application with name StrucID which runs Matlab. The App requires as input ...

Cerebral small vessel disease (SVD) may cause cognitive dysfunction. We tested the association between the combined presence of magnetic resonance imaging (MRI) features of SVD and cognitive ability in older age. Cognitive testing and brain MRI were performed in 680 older participants. MRI presence of lacunes, white matter hyperintensities, microbleeds, and perivascular spaces were summed in a ...