Inexact Newton methods on a vector supercomputer
The authors propose a modification of Newton's method for solving nonlinear systems \(F(x)= 0\), which allows to use the same Jacobian \(F'(x)\) repeatedly and to solve the equations for the correction \(F'(x) \Delta x= -F(x)\) only approximately. Such methods can be useful in cases where the costs for building the Jacobian are high. The authors also point out that forming and solving the equations can parallelize poorly, particularly for problems where the Jacobian is rather sparse. Two lemmas are given to establish local convergence and a theorem is presented that helps to determine the convergence order of this method. Three numerical examples show that the proposed method is able to achieve a much better performance on a vector supercomputer than the exact Newton method.
scientific article; zbMATH DE number 804740
scientific article