Iterative Methods for Solving Nonlinear Least Squares Problems
Victor L. Pereyra · SIAM Journal on Numerical Analysis · 1967
In many technical applications it is desired to f i t a nonlinear model t o a s e t of observations.t o determine a b e s t s e t of parameters in the l e a s t squares s e n s e . Several iterative techniques have been devised i n orderIn t h i s paper w e d i s c u s s conditions for convergence, and give error e s t i m a t e s for a c l a s s of methods, which includes as particular c a s e s some well known techniques.modified Newton's iterations for a suitable functional equation, and then a general theorem, first indicated by Bartle, is proved and applied to this particular case.The hypotheses are s e t in such a w a y that their checking by a n automatic computer i s made possible.It is shown t h a t those methods c a n be considered a s Some numerical examples are given.The main aim is to show that t h e automatic error estimation procedure works, rather than attempting t o optimize the computational s c h e m e .