Algorithm 14.1: Gauss-Newton method. More...

Functions
function	gaussNewton (in obj, in x0, in eps, in maxiter)
	Applies Gauss-Newton algorithm to solve $\min_x f(x)= \frac{1}{2} g(x)^T g(x)$ where $g:\mathbb{R}^n\to\mathbb{R}^m$ . More...

Detailed Description

Algorithm 14.1: Gauss-Newton method.

Implementation of algorithm 14.1 of [1]

Definition in file gaussNewton.m.

Function Documentation

Applies Gauss-Newton algorithm to solve

$\min_x f(x)= \frac{1}{2} g(x)^T g(x)$

where $g:\mathbb{R}^n\to\mathbb{R}^m$ .

Parameters

obj	the name of the Octave function defining g(x) and its gradient matrix. It should return a vector of size m and a matrix of size n x m.
x0	the starting point
eps	algorithm stops if $\\|\nabla g(x) g(x)\\| \leq \varepsilon$ .
maxiter	maximum number of iterations (Default: 100)

Returns: [solution,iteres,niter]; solution: local minimum of the function; iteres: sequence of iterates generated by the algorithm. It contains n+2 columns. Columns 1:n contains the value of the current iterate. Column n+1 contains the value of the objective function. Column n+2 contains the value of the norm of the gradient. It contains maxiter rows, but only the first niter rows are meaningful.; niter: total number of iterations