Displaying similar documents to “One iterative method concerning the solution of Dirichlet's problem”

Using successive approximations for improving the convergence of GMRES method

Jan Zítko (1998)

Applications of Mathematics

Similarity:

In this paper, our attention is concentrated on the GMRES method for the solution of the system ( I - T ) x = b of linear algebraic equations with a nonsymmetric matrix. We perform m pre-iterations y l + 1 = T y l + b before starting GMRES and put y m for the initial approximation in GMRES. We derive an upper estimate for the norm of the error vector in dependence on the m th powers of eigenvalues of the matrix T . Further we study under what eigenvalues lay-out this upper estimate is the best one. The estimate shows and...

On factorization method

Jiří Taufer (1966)

Aplikace matematiky

Similarity:

In this paper the method of factorization for boundary value problems of system of differential equations is generalized. The method described is successful providiny that the problem has a unique solution. Further the question of influence of errors resulting from numerical realization of the method on the solution is dealt with in the article.

Numerical solution of boundary value problems for selfadjoint differential equations of 2 n th order

Jiří Taufer (2004)

Applications of Mathematics

Similarity:

The paper is devoted to solving boundary value problems for self-adjoint linear differential equations of 2 n th order in the case that the corresponding differential operator is self-adjoint and positive semidefinite. The method proposed consists in transforming the original problem to solving several initial value problems for certain systems of first order ODEs. Even if this approach may be used for quite general linear boundary value problems, the new algorithms described here exploit...