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The low natural fertility of tropical soils and the mineralogy almost dominated by iron and aluminum oxides limit the availability of phosphorus (P) to the plants, causing negative impacts on soybean yield. Objective was to evaluate the effect of phosphate fertilization on soils with different maximum phosphorus adsorption capacities (PAC) in soybean development. The experiment was carried out under greenhouse conditions, using Red-yellow Latosol (RYL) and a Typic Hapludalf (TH) soil as substrate. The analyses were performed by a completely randomized experimental design in a 5 × 2 factorial arrangement with three replications. The treatments consisted of 5 doses of P applied, corresponding to 0, 1, 6, 12, and 24% of PAC of each soil. In the soil, the mineralogy of the clay fraction (hematite, goethite, gibbsite and kaolinite) and crystallographic attributes were characterized. In the plant, we evaluated growth and pod production. The PAC of the soils ranged from 220 to 650 mg dm -3 with higher value in the RYL associated to clayey oxidic mineralogy and texture in relation to the TH of kaolinite origin and sandy texture, where the higher energy of adsorption observed was to TH. Phosphorus application from 16 to 21% of PAC, independently of the soil, promotes the same pattern of response with improvements in soybean development evidenced by increases in P content in plant tissue, plant height, root volume and aerial dry mass.

RESUMONeste trabalho apresenta-se a otimização dos pesos das observações baseada em um problema de valor próprio inverso e dois métodos para a sua solução. O método de Newton clássico (aproximação linear) e o método quase-Newton-BFGS (BroydenFletcher-Goldfarb-Shanno) que usa de modelos quadráticos para minimizar uma função. Apresentam-se ainda os fundamentos da otimização dos pesos das observações geodésicas formuladas através da análise dos valores próprios da matriz de covariâncias dos parâmetros estimados. Os métodos propostos são aplicados em três redes geodésicas bidimensionais locais e os resultados analisados e discutidos.

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