Relationship between the inexact Newton method and the continuous analogy of Newton's method

Abstract

In this paper we propose two new strategies to determine the forcing terms that allow one to improve the efficiency and robustness of the inexact Newton method. The choices are based on the relationship between the inexact Newton method and the continuous analogy of Newton's method. With the new forcing terms, the inexact Newton method is locally \(Q\)-superlinearly and quadratically convergent. Numerical results are presented to support the effectiveness of the new forcing terms.

Keywords

• inexact Newton method
• continuous analogy of Newton's method