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Type of Document	Dissertation
Author	Rice, John Rischard
URN	etd-02102006-083607
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-02102006-083607
Title	The characterization of best nonlinear Tchebycheff approximations
Degree	PhD
Option	Mathematics
Advisory Committee	Advisor Name Title Arthur Erdelyi Committee Chair
Keywords	none
Date of Defense	1959-01-01
Availability	unrestricted
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.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    Rice_jr_1959.pdf 4.84 Mb 00:22:23 00:11:31 00:10:04 00:05:02 00:00:25