A Defense of the Karst Algorithm for Finding the Line of Best Fit under the L1 Norm.

Abstract

The methods proposed by Karst and Sharpe of fitting a line to a given set of points in the plane so as to minimize the sum of the absolute values of the deviations are examined by means of their linear programming formulations. For the single purpose of finding the optimal line the Karst procedure appears to be very efficient. If, as Sharpe suggests may sometimes be the case, the investigator is interested in the sensitivity of the minimum sum to changes in the slope parameter, then Sharpe's algorithm is preferred. The Karst algorithm is improved by incorporating into it the simplex stopping rule. The problem is generalized to permit arbitrary weightings of the deviations.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1977
Accession Number
ADA042691

Entities

People

  • Donald R. Schuette

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Classification
  • Computer Programming
  • Contracts
  • Curve Fitting
  • Equations
  • Evolutionary Algorithms
  • Iterations
  • Linear Programming
  • Mathematical Analysis
  • Mathematical Programming
  • Mathematics
  • North Carolina
  • Operations Research
  • United States
  • Wisconsin

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  • Approximation Theory.
  • Geotechnical Engineering.
  • Operations Research