β Scribed by Chong Li; Wen-Hong Zhang; Xiao-Qing Jin
No coin nor oath required. For personal study only.
generalized radius and center Lipschitz conditions with L average are introduced to investigate the convergence of Gauss-Newton's method for finding the nonlinear least squares solution of nonlinear equations. The radii of the convergence ball of Gauss-Newton's method and the uniqueness ball of the solution are estimated. Some applications are given.
π SIMILAR VOLUMES
Newton's method is based on a linear approximation of the function in a neighborhood of a solution point. It can be demonstrated that the error in the current iteration depends on the norm of second derivative. Instead using a higher-order approximation, the second derivative is used here to transfo
Under the hypotheses that nonlinear operators have (K,p)-Htilder-type continuous derivatives, exact estimates of the radius of the convergence ball of Newton's method and of the uniqueness ball of solution of equations are obtained.