Name
Title | ||
|---|---|---|
A Rayleigh–Ritz preconditioner for the iterative solution to large scale nonlinear problems |
Abstract | ||
|---|---|---|
The approximation to the solution of large sparse symmetric linear problems arising from nonlinear systems of equations is
considered. We are focusing herein on reusing information from previous processes while solving a succession of linear problems
with a Conjugate Gradient algorithm. We present a new Rayleigh–Ritz preconditioner that is based on the Krylov subspaces and
superconvergence properties, and consists of a suitable reuse of a given set of Ritz vectors. The relevance and the mathematical
foundations of the current approach are detailed and the construction of the preconditioner is presented either for the unconstrained
or the constrained problems. A corresponding practical preconditioner for iterative domain decomposition methods applied to
nonlinear elasticity is addressed, and numerical validation is performed on a poorly-conditioned large-scale practical problem. |
Year | DOI | Venue |
|---|---|---|
1998 | https://doi.org/10.1023/A:1016680306741 | Numerical Algorithms |
Keywords | Field | DocType |
conjugate gradient,Ritz values,superlinear convergence,Rayleigh matrix,Krylov subspaces,series of linear problems,65B99,65Y05 | Rayleigh–Ritz method,Conjugate gradient method,Nonlinear elasticity,Mathematical optimization,Nonlinear system,Preconditioner,Mathematical analysis,Superconvergence,Linear subspace,Mathematics,Domain decomposition methods | Journal |
Volume | Issue | ISSN |
17 | 3 | 1017-1398 |
Citations | PageRank | References |
9 | 1.05 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christian Rey | 1 | 9 | 1.05 |
| F. Risler | 2 | 18 | 1.93 |