A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Tensor structure applied to the least-squares method, revisited
Abstract The geometrical approach to the least-squares, based on differential geometry with tensor structure and notations, describes the adjustment theory in a simple and plausible manner. The development 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- or r-dimensional surfaces, where n is the number of observations, u is the number of parameters in the parametric method and r is the number of conditions in the condition method, with n=u+r. Connection is made to Hilbert spaces by demonstrating that the tensor approach to the least-squares is a classical case of the Hilbert-space approach.
Tensor structure applied to the least-squares method, revisited
Abstract The geometrical approach to the least-squares, based on differential geometry with tensor structure and notations, describes the adjustment theory in a simple and plausible manner. The development 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- or r-dimensional surfaces, where n is the number of observations, u is the number of parameters in the parametric method and r is the number of conditions in the condition method, with n=u+r. Connection is made to Hilbert spaces by demonstrating that the tensor approach to the least-squares is a classical case of the Hilbert-space approach.
Tensor structure applied to the least-squares method, revisited
BLAHA, Georges (author)
Bulletin Géodésique ; 58
1984
Article (Journal)
Electronic Resource
English
Tensor structure and the least squares
| Online Contents | 1979
European Regional Convergence Revisited: A Weighted Least Squares Approach
| Online Contents | 2009
Weighted total least squares applied to mixed observation model
| Online Contents | 2015
Weighted total least squares applied to mixed observation model
| Online Contents | 2016
Multi-dimensional moving least squares method applied to 3D elasticity problems
| Online Contents | 2013