Optimization theory and methods, which studies how the program or from a number of possi-ble ways to find the best solution. Optimization techniques In defense, industrial and agricultural production, transportation, finance, trade, management, and many other areas of scientific research has a wide range of applications. With the development of computers, optimization theory and algorithms in practical applications, is playing an increasing role.we analyzes the nonlinear least squares problems of the local convergence of Gauss-Newton's Methods, convergence rate and the corresponding radius of convergence. Inexact Gauss-Newton's methods, In addition to the conditions with weak Newton method instead of the strong future conditions, and the use of Matlab, computing, has been an ideal Results.Chapter III of this paper considers two local convergence theorem of Gauss-Newton's meth-ods. By applying the Holder continuous, Banach lemma on invertible on operators and affine Invariant condition, respectively, in the first Frchet-derivative and second Frchet-derivative, the Gauss-Newton's methods of local convergence theorems, and get the corresponding Convergence rate and convergence radius, the radius of convergence than in [1] to be large. Gauss-Newton's methods instead of using a weaker condition of convergence of Newton's methods conditions,Also obtained the corresponding estimate of the radius of convergence. |