Asynchronous Methods and Least Squares: An Example of Deteriorating Convergence

We use block iterative methods for solving linear least squares problems. The subproblems are solved asynchronously on a distributed memory multiprocessor. It is observed that increased number of processors results in deteriorating convergence. We illustrate the deteriorating convergence by some numerical experiments. The deterioration of the convergence can be explained by contamination of the residual. The residual is contaminated by old information. Our purpose is to reduce the effect of old information. The issues investigated here are the effect of the number of processors, the role of essential neighbors [8] and heterogeneous processors. We include two heuristics to identify the information to be discarded and reduce the effect of old information: a relaxation factor and synchronization. The characterization of old information remains as an open problem. 1 Introduction In this paper we use block iterative method for solving sparse linear least squares problems. A general framewo..

Deteriorating Convergence for Asynchronous Methods on Linear Least Squares Problems

. A block iterative method is used for solving linear least squares problems. The subproblems are solved asynchronously on a distributed memory multiprocessor. It is observed that an increased number of processors results in deteriorating rate of convergence. This deteriorating convergence is illustrated by numerical experiments. The deterioration of the convergence can be explained by contamination of the residual. Our purpose is to show that the residual is contaminated by old information. The issues investigated here are the effect of the number of processors, the role of essential neighbors, and synchronization. The characterization of old information remains an open problem. 1 Introduction In this paper, a block iterative method is used for solving sparse linear least squares problems. A general framework for this method is introduced by Dennis and Steihaug [4], and the preliminary tests in [4] indicate that this method leads quickly to cheap solutions of limited accura..

Capillary microarchitectural changes in Cushing's syndrome

Purpose: Macrovascular alterations are prominent in Cushing's syndrome (CS). Microvascular abnormalities are yet to be established. This cross-sectional observational study aimed to evaluate microvascular changes in nailfold capillaries and their association with disease status and carotid intima-media thickness (CIMT) as a marker of atherosclerosis. Methods: A total of 70 patients with CS [46 (65.7%) ACTH-dependent pituitary adenoma and 24 (34.3%) adrenocortical adenomas] and 100 healthy controls were enrolled. The microvascular structure was evaluated using nailfold video-capillaroscopy (NVC). Results: The median number of capillaries was less [10 mm (IQR: 2, min-max:7-14) vs. 11 mm (IQR: 2, minmax:9-19) (p < 0.001)], the median limb diameter and capillary width were wider in the CS group than in the controls (p = 0.016 and p = 0.002, respectively). Microhemorrhages within limited areas were more frequent in the CS group than in the controls (p = 0.046). Observed capillary changes were similar among the patients with CS with remission or active disease. CIMT levels were higher in the CS group than in the controls and similar in subjects with active disease and remission. Univariate logistic regression analyses revealed that the number of capillaries and capillary widths were associated with body mass index (BMI), the presence of type 2 diabetes mellitus, HbA1c, and CIMT. Conclusion: Morphologic alterations present similarly in nailfold capillaries in subjects with CS regardless of disease status, resembling changes in chronic atherosclerotic diseases. Microvascular changes in nailfold capillaries measured using NVC can be used as a marker in the assessment of cardiovascular risk in patients with CS