Solution of nonlinear algebraic equation systems and single and multiresponse nonlinear parameter estimation problems

A solver for systems of nonlinear algebraic equations and a nonlinear parameter estimation package are presented.; Both programs are based on Newton's method. The algebraic equation solver was used as a development tool to test features which could be beneficial to the nonlinear regression package. The most significant finding was that application of a robust nonmonotonic step acceptance criterion could improve performance. Several other features were tested leading to the development of a flexible nonlinear equation solver NNES (Nonmonotonic Nonlinear Equation Solver).; The package GREG (Generalized Regression) was designed to solve three classes of nonlinear regression problems: single-response, multiresponse with complete or block-rectangular data and multiresponse with missing observations. Minimization criteria for all cases were based on Bayesian principles. A new version of the Jeffreys prior was derived for the missing observations case.; The complexity of the derivatives of the new version of the Jeffreys prior made it too inefficient to be used when there are more than five responses. Because of this difficulty another criterion for the missing-observations problem based on the prior for the complete-data case was included in the package.