In this paper, a detailed description of CG for evaluating eigenvalue problems by minimizing the Rayleigh quotient is presented from both theoretical and computational viewpoints. Three variants of CG together with their asymptotic behaviours and restarted schemes are discussed. In addition, it is s
Efficient Computational Schemes of the Conjugate Gradient Method for Solving Linear Systems
β Scribed by Stepan G. Mulyarchik; Stanislav S. Bielawski; Andrew V. Popov
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 444 KB
- Volume
- 110
- Category
- Article
- ISSN
- 0021-9991
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π SIMILAR VOLUMES
Comparisons have been made between relaxation methods and certain preconditioned conjugate gradient techniques for solving the system of linear equations arising from the finite-difference form of the linearized Poisson-Boltzmann equation. The incomplete Cholesky conjugate gradient (ICCG) method of
Parallel preconditioners are considered for improving the convergence rate of the conjugate gradient method for solving sparse symmetric positive definite systems generated by finite element models of subsurface flow. The difficulties of adapting effective sequential preconditioners to the parallel
## Abstract We discuss the efficiency of the conjugate gradient (CG) method for solving a sequence of linear systems; __Au__^__n__+1^ = __u__^__n__^, where __A__ is assumed to be sparse, symmetric, and positive definite. We show that under certain conditions the Krylov subspace, which is generated