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Mathematics of Computation

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Computing the strict Chebyshev solution of overdetermined linear equations

Author: Nabih N. Abdelmalek
Journal: Math. Comp. 31 (1977), 974-983
MSC: Primary 65F20
MathSciNet review: 0445803
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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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Keywords: Discrete linear Chebyshev approximation, strict Chebyshev approximation, overdetermined linear equations, linear programming
Article copyright: © Copyright 1977 American Mathematical Society

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