The Characterization of Best Nonlinear Tchebycheff Approximations

Author: Rice, John Rischard

Year: 1959

Degree: Dissertation (Ph.D.)

Advisor: Erdélyi, Arthur

Committee Member: Unknown, Unknown

Option: Mathematics

DOI: 10.7907/J15M-W835

Abstract

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Consider a continuous function, F([...]) of n parameters and [...]. Such a function is said to have Property NS if the following theorem is valid for every continuous function, f(x):

THEOREM: F([...]) is a best approximation to f(x) if and only if there are n+1 distinct points, [...], such that [...].

Depending an the basic assumptions on F, several sets of necessary and sufficient conditions are given for F to have Property NS. These conditions involve unisolvence and related concepts. The definition of Property NS is generalized and necessary and sufficient conditions on F are given for F to have this generalized property. The latter theory includes most common nonlinear approximating functions.

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