The Characterization of Best Nonlinear Tchebycheff Approximations

[摘要] 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 generalizedproperty. The latter theory includes most common nonlinear approximating functions.

[发布机构] University:California Institute of Technology;Department:Physics, Mathematics and Astronomy

[关键词] Mathematics