A Geometric Property of the Least Squares Solution of Linear Equations

Abstract

The authors derive an explicit determinantal formula for the least squares (LS) solution of an overdetermined system of linear equations. From this formula it follows that the LS solution lies in the convex hull S of points, each of which is a solution of a square subsystem of the whole system. The results are extended to weighted LS solution; it is shown that the convex hull S in which the solution must lie is independent of the weighting matrix.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1988
Accession Number
ADA201342

Entities

People

  • Aharon Ben-tal
  • Marc Teboulle

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Business Administration
  • Classification
  • Computations
  • Convex Sets
  • Equations
  • Linear Programming
  • Mathematics
  • New York
  • Notation
  • Security
  • Theorems
  • Universities

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Graph Algorithms and Convex Optimization.
  • Linear Algebra