Abstract
This paper proposes a preconditioner for the conjugate gradient method (CG) that is designed for solving systems of equations Acursive Greek chi = bi with different right-hand-side vectors or for solving a sequence of slowly varying systems Akcursive Greek chi = bk. The preconditioner has the form of a limited memory quasi-Newton matrix and is generated using information from the CG iteration. The automatic preconditioner does not require explicit knowledge of the coefficient matrix A and is therefore suitable for problems where only products of A times a vector can be computed. Numerical experiments indicate that the preconditioner has most to offer when these matrix-vector products are expensive to compute and when low accuracy in the solution is required. The effectiveness of the preconditioner is tested within a Hessian-free Newton method for optimization and by solving certain linear systems arising in finite element models.
Original language | English (US) |
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Pages (from-to) | 1079-1096 |
Number of pages | 18 |
Journal | SIAM Journal on Optimization |
Volume | 10 |
Issue number | 4 |
DOIs | |
State | Published - 2000 |
Keywords
- Conjugate gradient method
- Hessian-free Newton method
- Limited memory method
- Preconditioning
- Quasi-Newton method
ASJC Scopus subject areas
- Software
- Theoretical Computer Science