Curvilinear interpolation: hyperbola with a linear term

Abstract

This paper illustrates a method for interpolating curvilinear data by means of the hyperbola plus a linear term. The method is based on the least squares principle. It requires a minimum of four curvilinear data and it is easy to apply.

Curve fitting with double-exponential equations

“…Such equations should reproduce the original data and interpolate real numbers using real numbers. If there is no complete solution set try another approach to generate an interpolating equation [1][2][3].…”

“…The list below contains functions that are applied to [1,2,3,4,5] and [1,2,3,4,5,6], respectively, to generate five-and six-member data sets.…”

“…Recent papers in This Journal illustrate curvilinear interpolation by means of hyperbolas and exponentials [1,2,3]. For five and six equidistant, curvilinear data, the exponential interpolating forms are Eqs.…”

“…For five and six equidistant, curvilinear data, the exponential interpolating forms are Eqs. (1) and (2)…”

“…Let six curvilinear (x,y) data be(1,49),(2,81),(3,141),(4,269), (5,569), (6, 1321). The sum of their squared deviations is Eq.…”