Preconditioned conjugate gradient methods applied to certain symmetric linear systems
- 1 January 1986
- journal article
- research article
- Published by Taylor & Francis in International Journal of Computer Mathematics
- Vol. 19 (2) , 177-200
- https://doi.org/10.1080/00207168608803513
Abstract
Preconditioned conjugate gradient methods for solving symmetric linear systems resulting from high order discretization techniques for elliptic partial differential equations are investigated. The preconditionings are based on an incomplete LU factorization to another matrix that arises from the application of a lower order approximation to the same elliptic equation. The use of R similarity transformation to estimate the extreme eigenvalues and the condition numbers of the linear systems is described. The efficiency and effectiveness of the preconditioned algorithms are demonstrated by the computational experiments.Keywords
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