Solving Nonlinear Least Squares Problems with B-Spline Functions

In this paper a method for solving nonlinear least squares problems is presented. Ordinary least squares methods for solving these problems with linear methods, like polynomials and trigonometric least squares functions, are not suitable to follow nonlinear behavior of the desired solution. Nonlinear least squares methods are very dependent on initial estimation. B-spline functions are not nonlinear related to unknown parameters, but can behave as nonlinear functions and need not an initial estimation. Numerical experiments show that B-spline functions, due to piecewise polynomial character and smoothness, are a very useful tool for solving nonlinear least squares problems.

Keywords:

Least squares method , Spline functions , B-spline functions