Abstract
A nonlinear conjugate gradient method has been introduced and analyzed by J.W. Daniel. This method applies to nonlinear operators with symmetric Jacobians. Orthomin(1) is an iterative method which applies to nonsymmetric and definite linear systems. In this article we generalize Orthomin(1) to a method which applies directly to nonlinear operator equations. Each iteration of the new method requires the solution of a scalar nonlinear equation. Under conditions that the Hessian is uniformly bounded away from zero and the Jacobian is uniformly positive definite the new method is proved to converge to a globally unique solution. Error bounds and local convergence results are also obtained. Numerical experiments on solving nonlinear operator equations arising in the discretization of nonlinear elliptic partial differential equations are presented.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.