Analysis Linking the Tensor Structure to the Least-Squares Method.

Abstract

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 n=u+r. Other methods are not treated here.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1984
Accession Number
ADA142159

Entities

People

  • G. Blaha

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Coordinate Systems
  • Covariance
  • Data Science
  • Differential Geometry
  • Earth Sciences
  • Geometry
  • Hilbert Space
  • Information Science
  • Least Squares Method
  • Mathematical Models
  • Models
  • Probability Distributions
  • Statistics
  • Tensor Analysis
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Graph Algorithms and Convex Optimization.
  • Regression Analysis.

Technology Areas

  • Space