Nonlinearly preconditioned Krylov subspace methods for discrete Newton algorithms
We propose an algorithm for implementing Newton's method for a general nonlinear system f(x) = 0 where the linear systems that arise at each step of Newton's method are solved by a preconditioned Krylov subspace iterative method. The algorithm requires only function evaluations and does not require the evaluation or storage of the Jacobian matrix. Matrix-vector products involving the Jacobian matrix are approximated by directional differences. We develop a framework for constructing preconditionings for this inner iterative method which do not reference the Jacobian matrix explicitly. We derive a nonlinear SSOR type preconditioning which numerical experiments show to be as effective as the linear SSOR preconditioning that uses the Jacobian explicitly.
- Research Organization:
- Yale Univ., New Haven, CT (USA). Dept. of Computer Science
- DOE Contract Number:
- AC02-81ER10996
- OSTI ID:
- 5071100
- Report Number(s):
- DOE/ER/10996-T1; ON: DE84010407
- Country of Publication:
- United States
- Language:
- English
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