Computing the strict Chebyshev solution of overdetermined linear equations

Author:
Nabih N. Abdelmalek

Journal:
Math. Comp. **31** (1977), 974-983

MSC:
Primary 65F20

DOI:
https://doi.org/10.1090/S0025-5718-1977-0445803-8

MathSciNet review:
0445803

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Abstract | References | Similar Articles | Additional Information

Abstract: A method for calculating the strict Chebyshev solution of overdetermined systems of linear equations using linear programming techniques is described. This method provides: (1) a way to determine, for the majority of cases, all the equations belonging to the characteristic set, (2) an efficient method to obtain the inverse of the matrix needed to calculate the strict Chebyshev solution, and (3) a way of recognizing when an element of the Chebyshev solution equals a corresponding element of the strict Chebyshev solution. As a result, in general, the computational effort is considerably reduced. Also the present method deals with full rank as well as rank deficient cases. Numerical results are given.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0445803-8

Keywords:
Discrete linear Chebyshev approximation,
strict Chebyshev approximation,
overdetermined linear equations,
linear programming

Article copyright:
© Copyright 1977
American Mathematical Society