A method of exponential separation applicable to small computers

Abstract

A method has been developed for separation of the components of multicompartment exponentials which operates on a small computer. It seems free of many of the difficulties of other methods and provides a reasonable test for the number of components.

A Weighted Least-Squares Technique for the Analysis of Kinetic Data and Its Application to the Study of Renal 133 Xenon Washout in Dogs and Man

“…There have been a number of proposals advanced and computer programs written (17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33) which attempt to estimate the parameters of nonlinear equations. However, among those using weighted least-squares parameter estimation none appear to combine the rapid and reliable Marquardt convergence technique with both residual error testing to select among models and tests on the validity of the fit to the data.…”

“…Another technique, Prony's method (19,20), expresses the exponential equation as a polynomial. The coefficients of the polynomial are estimated by a linear least-squares technique, and then the parameters of the original exponential equation are estimated by back substitution.…”

Εφαρμογη Της Διαμερισματικης Αναλυσης Στην Ιατρικη Με Τη Χρηση Ηλεκτρονικου Υπολογιστη

“…Γιά την προσαρμογή της καμπύλης στα πειραματικά ,δεδομένα προτιμήθηκε μία αναλυτική μέθοδος, η οποία βασίζεται στη μέθοδο Prony (Householder 1949, Hildebrand 1956, Lanczos 1956, Simon 1970. Η ιδέα της χρησιμοποίησης μίας επαναληπτικής μεθόδου εγκαταλείφθηκε εντελώς, γιατί το πρόγραμμα προορίζονταν γιά να τρέχει σε απλούς υπολογιστές, μέτριων δυνατοτήτων και μία επαναληπτική μέθοδος απαιτεί μεγάλη υπολογιστική ισχύ.…”