Preconditioned conjugate gradient methods applied to certain symmetric linear systems

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:

• Conjugate gradient method
• preconditionings
• high order approximations
• 27-points difference scheme
• extreme eigenvalues
• elliptic P.D.E.s

C.R. Categories:

• G.1.8
• G.1.3

This work was supported by the Natural Sciences and Engineering Research Council of Canada Grant U0375.

This work was supported by the Natural Sciences and Engineering Research Council of Canada Grant U0375.

Notes

This work was supported by the Natural Sciences and Engineering Research Council of Canada Grant U0375.