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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Least squares approximations

Wiener, Marvin January 1962 (has links)
Thesis (M.A.)--Boston University / This paper, utilizing the properties of Vector spaces, describes an approach to polynomial approximations of functions defined analytically or by a set of observations over some interval. If the function and its approximation are both considered tobe elements of a linear normed vector space, a weighted sum or integral of the square of the discrepancy between the function and its approximation is to be a minimum. When this condition is satisfied, and depending upon the interval of interest, the polynomial approximation to the function becomes either the Legendre, Chebyshev, Laguerre, or hermite approximation formulas. An investigation into the properties and applications of these formulas is included, and it is shown that these formulas give the best polynomial approximations to certain functions in the sense of least squares.

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