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# Accession Number:

## AD0804502

# Title:

## APPLIED APPROXIMATION THEORY.

# Descriptive Note:

## Technical rept. Jul 65-Jul 66,

# Corporate Author:

## AIR FORCE WEAPONS LAB KIRTLAND AFB NM

# Report Date:

## 1966-11-01

# Pagination or Media Count:

##
102.0

# Abstract:

## Many methods of approximating tabular data with continuous functions are available. The method one selects depends upon which of the following motives apply 1 Data smoothing may be desired if the data are noisy 2 Data amplification i.e., increasing the tabular data by interpolation techniques like the spline fit may be used when the data come from an exceptionally smooth function 3 Data reduction may be desired if the data table is too large or it is desired to store the essence of the information as the coefficients of some continuous function 4 Data representation may be desired when one is attempting to determine if certain data conforms to a physical law or when one is attempting to postulate a physical law from certain data. From these situations, certain notions of goodness of fit arise. In attaining the best fit one may be led to the methods of least mean squares, minimax, linear programming, quadratic programming. In some cases fits which are nonlinear in their coefficients can be very efficient. The exchange method may be used to find the minimax fit in very general circumstances. If the continuous function satisfies certain conditions specified in text which are weaker than unisolvence, the the exchange method finds the minimax. Computer programs which automate these methods are available. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#