Polynomials associated with exponential regression

Abstract

Abstract. Fitting exponentials a + be cx to data by the least squares method is discussed. It is shown how the polynomials associated with this problem can be factored. The closure of the set of this type of functions defined on a finite domain is characterized and an existence theorem derived. If there is such a minimum, then the partial derivatives with respect to a, b, R are equal to zero at a point at which the minimum is located and, if b = 0, we are led to the equationsIf there exists a solution to this system of equations for some R, then a, b, −1 are the coefficients of a linear combination of the columns of the matrixyielding the zero vector.2000 Mathematics Subject Classification: 62J02, 65D10, 65D15.