An Efficient Implementation of the Gauss-Newton Method Via Generalized Krylov Subspaces

The solution of nonlinear inverse problems is a challenging task in numerical analysis. In most cases, this kind of problems is solved by iterative procedures that, at each iteration, linearize the problem in a neighborhood of the currently available approximation of the solution. The linearized problem is then solved by a direct or iterative method. Among this class of solution methods, the Gauss-Newton method is one of the most popular ones. We propose an efficient implementation of this method for large-scale problems. Our implementation is based on projecting the nonlinear problem into a sequence of nested subspaces, referred to as Generalized Krylov Subspaces, whose dimension increases with the number of iterations, except for when restarts are carried out. When the computation of the Jacobian matrix is expensive, we combine our iterative method with secant (Broyden) updates to further reduce the computational cost. We show convergence of the proposed solution methods and provide a few numerical examples that illustrate their performance

Effect of dietary Acrocomia aculeata kernel oil rich in medium chain fatty acids on type 2 diabetic rats.

This study evaluated the effects of dietaries formulated with kernel oil of Acrocomia aculeata (AKO), rich in medium chain fatty acids (MCFA), as partial substitute of carbohydrate calories upon blood glucose, lipid profile, insulin secretion and insulin sensitivity in diabetic rats. Overall, the dietary with any AKO dose reduced hyperglycemia, ameliorated insulin secretion, lowered insulin resistance by model HOMA-IR and HOMA-Beta and augmented pancreatic beta cells functionality, restored the number of pancreatic Beta-cell in the diabetic rats and increased it in the non-diabetic rats. In addition, AKO fed rats showed reducing triglycerides, lower density lipoprotein-cholesterol and increasing high density lipoprotein-cholesterol levels, and improved hepatic function markers. Those findings suggest AKO was effective to ameliorate the health of diabetic rats.On-line first

Cluster randomized trial assessing the effects of rapid ethical assessment on informed consent comprehension in a low-resource setting

Background Maximizing comprehension is a major challenge for informed consent processes in low-literacy and resource-limited settings. Application of rapid qualitative assessments to improve the informed consent process is increasingly considered useful. This study assessed the effects of Rapid Ethical Assessment (REA) on comprehension, retention and quality of the informed consent process. Methods A cluster randomized trial was conducted among participants of HPV sero-prevalence study in two districts of Northern Ethiopia, in 2013. A total of 300 study participants, 150 in the intervention and 150 in the control group, were included in the study. For the intervention group, the informed consent process was designed with further revisions based on REA findings. Informed consent comprehension levels and quality of the consent process were measured using the Modular Informed Consent Comprehension Assessment (MICCA) and Quality of Informed Consent (QuIC) process assessment tools, respectively. Result Study recruitment rates were 88.7 % and 80.7 % (p = 0.05), while study retention rates were 85.7 % and 70.3 % (p < 0.005) for the intervention and control groups respectively. Overall, the mean informed consent comprehension scores for the intervention and control groups were 73.1 % and 45.2 %, respectively, with a mean difference in comprehension score of 27.9 % (95 % CI 24.0 % - 33.4 %; p < 0.001,). Mean scores for quality of informed consent for the intervention and control groups were 89.1 % and 78.5 %, respectively, with a mean difference of 10.5 % (95 % CI 6.8 -14.2 %; p < 0.001). Conclusion Levels of informed consent comprehension, quality of the consent process, study recruitment and retention rates were significantly improved in the intervention group. We recommend REA as a potential modality to improve informed consent comprehension and quality of informed consent process in low resource settings

A general framework for ADMM acceleration

The Alternating Direction Multipliers Method (ADMM) is a very popular algorithm for computing the solution of convex constrained minimization problems. Such problems are important from the application point of view, since they occur in many fields of science and engineering. ADMM is a powerful numerical tool, but unfortunately its main drawback is that it can exhibit slow convergence. Several approaches for its acceleration have been proposed in the literature and in this paper we present a new general framework devoted to this aim. In particular, we describe an algorithmic framework that makes possible the application of any acceleration step while still having the guarantee of convergence. This result is achieved thanks to a guard condition that ensures the monotonic decrease of the combined residual. The proposed strategy is applied to image deblurring problems. Several acceleration techniques are compared; to the best of our knowledge, some of them are investigated for the first time in connection with ADMM. Numerical results show that the proposed framework leads to a faster convergence with respect to other acceleration strategies recently introduced for ADMM

An Efficient Implementation of the Gauss–Newton Method Via Generalized Krylov Subspaces

The solution of nonlinear inverse problems is a challenging task in numerical analysis. In most cases, this kind of problems is solved by iterative procedures that, at each iteration, linearize the problem in a neighborhood of the currently available approximation of the solution. The linearized problem is then solved by a direct or iterative method. Among this class of solution methods, the Gauss–Newton method is one of the most popular ones. We propose an efficient implementation of this method for large-scale problems. Our implementation is based on projecting the nonlinear problem into a sequence of nested subspaces, referred to as Generalized Krylov Subspaces, whose dimension increases with the number of iterations, except for when restarts are carried out. When the computation of the Jacobian matrix is expensive, we combine our iterative method with secant (Broyden) updates to further reduce the computational cost. We show convergence of the proposed solution methods and provide a few numerical examples that illustrate their performance