Analysis Local Convergence of Gauss-Newton Method

The Gauss-Newton method is a very efficient, simple method used to solve nonlinear least-squares problems. This can be seen as a modification of the newton method to find the minimum value of a function. In solving nonlinear problems, the Gauss Newton Algorithm is used to minimize the sum of quadratic function values, which in its completion does not require the calculation or estimate of the derivatives of the two functions f (x) hence numerically more efficient with direct or iterative processes. The Gauss Newton method studied in this study is restricted to functions of one or two variables. The results of Gauss Newton's method analysis consisted of convergence at simple roots and multiple roots. Newton's method often converges quickly, especially when the iteration begins to be close enough to the desired root. However, if iteration begins far from the searched root, this method can be missed without warning. Implementation of this method usually detects and overcomes the convergence failures.