A Study on Some Methods of Interpolation Mathematical Representation of Data

Abstract

This thesis titled A Study on Some Methods of Interpolation: Mathematical Representation of newlineData is based on the research woks on deriving / developing / finding out of some formulas and newlinemethods of representing a set of numerical data on a pair of variables by mathematical curves. newlineSome of the existing methods of interpolation have been used in deriving / developing / finding newlineout the formulas and the methods aimed in the study. Therefore, the history of the development newlineof the methods of interpolation has been outlined briefly in the following section. Moreover, newlinethe motivation of this research and an overview of the research works done in this study have newlinebeen presented in the next two subsequent sections. newlineIn practical situation, it is often necessary to find out the value of a function corresponding to newlinesome value of the dependent variable from a set of given (or known) values of the function newlinecorresponding to a set of values of the independent variable. If the value of the independent newlinevariable for which the corresponding value of the function is to be determined lie within the newlinetwo extreme values (i.e. the maximum value and the minimum value) of the given values of newlinethe independent variable then determination of the value of the function is called interpolation newlinewhile if the value of the independent variable for which the corresponding value of the function newlineis to be determined lie outside the two extreme values then determination of the value of the newlinefunction is called extrapolation [Hummel (1947), Erdos and Turan (1938) et al]. A number of newlineformulas for interpolation have already been developed by renowned scientists. newline