Generation and Use of Orthogonal Polynomials for Data-Fitting with a Digital Computer

Abstract

the yk(X,) f,. cannot ordinarily all be made 0 simultaneously. When they cannot, the m conditions (2) compete with one another, and the numerical analyst must somehow take account of this in order to formulate a problem of data-fitting. The m numbers e, = Yk(X,) are the m components of an error vector e. Since the x,, and f,, are regarded as fixed, the vector e depends only on the parameters t(7k), , tk. Each common method for dealing with the competing requirements (2) corresponds to the selection of a norm 11 e 11 for the vector e. The two norms most frequently considered are the minimax norm