Stepwise nonlinear regression on sequentially arriving data

Algebraic aspects of combining (as applied to nonlinear regression problems) recursive algorithms of estimation and iterative methods of nonlinear optimization in cases of increasing number of parameters and increasing data arrays are considered. The results are formulated in recursive-iterative procedures of the Gauss - Newton method with pseudoinversion for stepwise nonlinear regression and for the recursive nonlinear least squares method. The Greville recursive algorithm of matrix pseudoinversion underlies these procedures.