NITSOL: A Newton iterative solver for nonlinear systems

Conference · Tue Dec 31 04:00:00 EST 1996

DOI:https://doi.org/10.1137/S1064827596303843· OSTI ID:433349

Pernice, M ^[1]; Walker, H F ^[2]

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1. Univ. of Utah, Salt Lake City, UT (United States)
2. Utah State Univ., Logan, UT (United States)

Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.

• Research Organization: Front Range Scientific Computations, Inc., Lakewood, CO (United States)
• DOE Contract Number: FG03-94ER25221
• OSTI ID: 433349
• Report Number(s): CONF-9604167--Vol.1; ON: DE96015306; CNN: Grant DMS-9400217
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGEBRA
ALGORITHMS
DESIGN
ITERATIVE METHODS
NEWTON METHOD
NONLINEAR PROBLEMS