Analysis Linking the Tensor Structure to the Least-Squares Method.
NOVA UNIV OCEANOGRAPHIC CENTER DANIA FL
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One of the main purposes of the geometrical approach to the least-squares adjustment as presented herein is to describe the adjustment theory in a simple and plausible way and, at the same time, to establish a niche for such an approach in a field that has been explored decades ago and then again in recent years. This development is based on differential geometry with tensor structure and notations. In expressing the desired tensor relations, it relies heavily on orthonormal space and surface vectors and on the extrinsic properties of surfaces linking the two kinds of vectors. In order to relate geometry to adjustments, the geometrical concepts are extended to an n-dimensional space and u-dimensional or r-dimensional surfaces, where n is the number of observations, u is the number of parameters in the parametric or observation equation method and r is the number of condition equations in the condition method, with nur. Other methods are not treated here.
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