New preconditioner updates in Newton-Krylov methods for nonlinear systems

Porcelli M., Bellavia S., Morini B.

Large scale optimization  Nonlinear otimization 

We address the problem of preconditioning sequences of large sparse indefinite systems of linear equations arising in the solution of large nonlinear systems via Newton-Krylov methods. We present two new strategies to construct approximate updates of a factorized preconditioner for a reference matrix of the sequence. Both updates are based on the availability of an incomplete factorization for one matrix of the sequence and differ in the approximation of the so-called ideal updates. Furthermore, nearly matrix-free implementations are discussed.

Source: 11th EUROPT Workshop on Advances in Continuous Optimization, Firenze, 26-28 Giugno 2013