Curvilinear interpolation using an exponential and a linear term

Abstract

This paper illustrates methods for interpolating curvilinear data using an exponential or an exponential plus a linear term. The methods are based on the least-squares principal. They require a minimum of three or four data, respectively.

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.…”

“…3and let it operate on the five numbers 1, 2, 3, 4, 5, respectively. The five (x,y) trial curvilinear data are thus (1,29), (3,51), (3,101), (4,219), (5,509), respectively. The sum of their squared deviations, denoted ∑, is Eq.…”

“…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.…”

“…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.…”