The Convergence of the Ben-Israel Iteration for Nonlinear Least Squares Problems

  title={The Convergence of the Ben-Israel Iteration for Nonlinear Least Squares Problems},
  author={Paul T. Boggs},
Ben-Israel [ 1 ] proposed a method for the solution of the nonlinear least squares problem m'mx^j^\\F(x)\\2 where F: D C R —► R . This procedure takes the form xk,x = xk — F'(xk) F(xk) where F'(xk) denotes the Moore-Penrose generalized inverse of the Fre'chet derivative of F. We give a general convergence theorem for the method based on Lyapunov stability theory for ordinary difference equations. In the case where there is a connected set of solution points, it is often of interest to determine… CONTINUE READING


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