The Characterization of Best Nonlinear Tchebycheff Approximations

Citation

Rice, John Rischard (1959) The Characterization of Best Nonlinear Tchebycheff Approximations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/J15M-W835. https://resolver.caltech.edu/CaltechETD:etd-02102006-083607

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. 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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