Choosing the forcing terms in an inexact Newton method

Journal Article · Mon Jan 01 04:00:00 EST 1996 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/0917003· OSTI ID:218521

Eisenstat, S C ^[1]; Walker, H F ^[2]

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1. Yale Univ., New Haven, CT (United States). Dept. of Computer Science
2. Utah State Univ., Logan, UT (United States). Dept. of Mathematics and Statistics

An inexact Newton method is a generalization of Newton`s method for solving F(x) = 0, F:R{sup n}{r_arrow}R{sup n}, in which, at the kth iteration, the step s{sub k} from the current approximate solution x{sub k} is required to satisfy a condition {vert_bar}{vert_bar}F(x{sub k} + F{prime}(x{sub k})s{sub k}{vert_bar}{vert_bar} {le} {eta}{sub k}{vert_bar}{vert_bar}F(x{sub k}){vert_bar}{vert_bar} for a ``forcing term`` {eta}{sub k}. In typical applications, the choice of the forcing terms is critical to the efficiency of the method and can affect robustness as well. Promising choices of the forcing terms are given, their local convergence properties are analyzed, and their practical performance is shown on a representative set of test problems.

• Sponsoring Organization: USDOE
• DOE Contract Number: FG02-92ER25136; FG03-94ER25221
• OSTI ID: 218521
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 1 Vol. 17; ISSN SJOCE3; ISSN 1064-8275
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ACCURACY
BOUNDARY CONDITIONS
CONVERGENCE
FORCING FUNCTIONS
NEWTON METHOD
PERFORMANCE