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Linear preconditioning conjugate method

In terms of the computational work per outer Newton step k), TN methods based on preconditioned conjugate gradient require a Hessian-vector product (Hd) at each inner loop iteration, and one solution of a linear system Mz = r where M is the preconditioner. Since M may be sparse, this linear solution often takes a very small percentage of the total CPU time (e.g., <3% ). The benefits of faster convergence generally far outweigh these costs. [Pg.1152]

In the work of Lindborg et al [119], the resulting linear equation systems were solved with preconditioned Krylov subspace projection methods [166]. The Poisson equation was solved by a conjugate gradient (CG)-solver, while the other transport equations were solved using a bi-conjugate gradient (BCG)-solver which can handle also non-symmetric equations systems. The solvers were preconditioned with a Jacobi preconditioner. [Pg.1074]


See other pages where Linear preconditioning conjugate method is mentioned: [Pg.2337]    [Pg.49]    [Pg.2337]    [Pg.201]    [Pg.241]    [Pg.3700]    [Pg.142]    [Pg.56]    [Pg.34]    [Pg.606]    [Pg.618]    [Pg.196]    [Pg.1250]    [Pg.1152]   
See also in sourсe #XX -- [ Pg.43 ]




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Conjugate method

Conjugation methods

Linear conjugation

Linear methods

Linearized methods

Preconditioning

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