Projection operators for the conjugate gradient method in case of solving finite difference equations in domains of a complicated form. (Russian. English summary) Zbl 0859.65027
The paper describes three algorithms for the construction of initial approximations for the solution of systems of linear algebraic equations by the preconditioned conjugate gradient method. The considered linear systems arise from a finite difference approximation to selfadjoint boundary value problems and the initial approximations are constructed making use of different orthogonal projectors. Algorithms are tested on a model problem which is taken from modelling of semiconductors.
Reviewer: R.Blaheta (Ostrava)
MSC:
65F10 | Iterative numerical methods for linear systems |
65F35 | Numerical computation of matrix norms, conditioning, scaling |
65N06 | Finite difference methods for boundary value problems involving PDEs |
35J25 | Boundary value problems for second-order elliptic equations |
35Q60 | PDEs in connection with optics and electromagnetic theory |
78A55 | Technical applications of optics and electromagnetic theory |