Generalized extrapolation principle and convergence of some generalized iterative methods

AbstractTo solve the linear system Ax = b, this paper presents a generalized extrapolated method by replacing the extrapolation parameter ω with the diagonal matrix Ω, and systematically gives the basic results for its convergence. Based upon these results, the paper considers the convergence of the GJ and GAOR iterative methods and, using the set of the equimodularized diagonally similar matrices defined here, gives some new further convergence results for H-matrices and their subclasses, strictly or irreducibly diagonally dominant matrices, which unify, improve, and extend previously given various results. Finally, conditions equivalent to the statement that A is a nonsingular H-matrix or a strictly (or an irreducibly) diagonally dominant matrix are given in connection with the GJ and GAOR methods

Phosphorus Sorption, Desorption and Availibility in Oxisols and Utisols as Influenced by Soil Aggregate Size

Phosphorus (P) limits food and fiber production in most regions of the tropics. The diagnosis and prediction of nutrient P requirements continues with low precision and high uncertainty. Some recent estimates suggest that predictions may be in error by as much as 50%. Initial data suggest that the high degree of soil aggregation common in highly weathered soils may affect P sorption. This study was conducted to determine the effects of soil aggregate size on P availability in order to improve P requirement prediction. The soils studied were highly weathered Typic Kandihumult (Leilehua), Anionic Acrudox (Kapaa), and Rhodic Eutrustox (Wahiawa) that represent high P sorption and a range in soil aggregation. Samples were collected from field plots of P experiments, where P had been applied 3-7.5 years before. For each soil, eight aggregate size fractions of < 0.053, 0.053-0.125, 0.125-0.25, 0.25-0.5, 0.5-1, 1-2, 2-4, and 4-6 mm were obtained using a dry-sieving method. For the Kapaa and Leilehua soils, sodium bicarbonate extractable P in aggregates increased up to 5-fold with decreasing aggregate size when P had been applied to soils. The extractable P did not increase with decreasing aggregate size on all soils where no P had been applied and even where P had been added to the Wahiawa soil. An incubation study showed that the increased extractable P was due to more sorbed P in small aggregates after P was added to a mixture of aggregates of different size. In contrast, P sorption decreased, and extractable P increased with increasing aggregate size after P was added to the separated aggregate fractions. The total P in soybean and lettuce shoots grown in larger aggregates (2-6 mm) was greater than in smaller aggregates (<0.5 mm) after P was added to the separated aggregate fractions. The reduced P sorption and increased P desorption with increasing aggregate size suggests that an improved prediction of the P buffer coefficients and P requirements in crop production systems could be achieved considering soil aggregate size distribution

An efficient probe of the cosmological CPT violation

We develop an efficient method based on the linear regression algorithm to probe the cosmological CPT violation using the CMB polarisation data. We validate this method using simulated CMB data and apply it to recent CMB observations. We find that a combined data sample of BICEP1 and BOOMERanG 2003 favours a nonzero isotropic rotation angle at $2.3\sigma$ confidence level, ie, $\Delta\alpha=-3.3 \pm1.4$ deg (68% CL) with systematics included.Comment: 10 pages, 5 figures, 2 tables. The published versio

Convergence properties of nonmonotone spectral projected gradient methods

AbstractIn a recent paper, a nonmonotone spectral projected gradient (SPG) method was introduced by Birgin et al. for the minimization of differentiable functions on closed convex sets and extensive presented results showed that this method was very efficient. In this paper, we give a more comprehensive theoretical analysis of the SPG method. In doing so, we remove various boundedness conditions that are assumed in existing results, such as boundedness from below of f, boundedness of xk or existence of accumulation point of {xk}. If ∇f(·) is uniformly continuous, we establish the convergence theory of this method and prove that the SPG method forces the sequence of projected gradients to zero. Moreover, we show under appropriate conditions that the SPG method has some encouraging convergence properties, such as the global convergence of the sequence of iterates generated by this method and the finite termination, etc. Therefore, these results show that the SPG method is attractive in theory