RIGOROUS CONVERGENCE ALGORITHM FOR FITTING A MONOEXPONENTIAL FUNCTION WITH A BACKGROUND TERM USING THE LEAST-SQUARES METHOD

An algorithm has been developed to analyze data that contain a single exponential function plus a background term, as described by the equation y equals b plus ae** minus **k**t. Since k is the only nonlinear parameter, the linear parameters a and b can be eliminated from the normal equations. This transforms the least-squares problem to one of finding the root of a transcendental equation. This can be approximated by applying the Newton-Raphson method inside an interval located by the Fibonacci order search. The features of the algorithm are given.