On error estimation in the conjugate gradient method and why it works in finite precision computations.
On Fixed Point Linear Equations.
On iterative methods of higher order for systems of linear algebraic equations
The paper is concerned with certain -degree iterative methods for the solution of linear algebraic systems. The successive approximation is determined by means of approximations , , , . In this article to each iterative method of the first degree some -degree iterative method is found in order to accelerate the convergence of the intial method.
On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations
In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.
On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations
In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.
On parallel two-stage methods for Hermitian positive definite matrices with applications to preconditioning.
On preconditioning Schur complement and Schur complement preconditioning.
On properties of some matrix splittings.
On selection of interface weights in domain decomposition methods
Different choices of the averaging operator within the BDDC method are compared on a series of 2D experiments. Subdomains with irregular interface and with jumps in material coefficients are included into the study. Two new approaches are studied along three standard choices. No approach is shown to be universally superior to others, and the resulting recommendation is that an actual method should be chosen based on properties of the problem.
On Semiiterative Methods Generated by Faber Polynomials.
On some extensions of the accelerated overrelaxation (AOR) theory.
On some Modifications of the Nekrassov Method for Numerical Solution of Linear Systems of Equations
A modification of the Nekrassov method for finding a solution of a linear system of algebraic equations is given and a numerical example is shown.* This paper is partly supported by project IS–M–4 of Department for Scientific Research, Paisii Hilendarski University of Plovdiv.
On the Analysis of the Unsymmetric Successive Overrelaxation Method when Applied to p-Cyclic Matrices.
On the choice of iteration parameters in the Stone incomplete factorization
The paper is concerned with the iterative solution of sparse linear algebraic systems by the Stone incomplete factorization. For the sake of clarity, the algorithm of the Stone incomplete factorization is described and, moreover, some properties of the method are derived in the paper. The conclusion is devoted to a series of numerical experiments focused on the choice of iteration parameters in the Stone method. The model problem considered showe that we can, in general, choose appropriate values...
On the choice of subspace for iterative methods for linear discrete ill-posed problems
Many iterative methods for the solution of linear discrete ill-posed problems with a large matrix require the computed approximate solutions to be orthogonal to the null space of the matrix. We show that when the desired solution is not smooth, it may be possible to determine meaningful approximate solutions with less computational work by not imposing this orthogonality condition.
On the Condition Number of some Gram Matrices Arising from Least Squares Approximation in the Complex Plane.
On the convergence of a modified block SOR algorithm.
On the convergence of a multicomponent alternating direction difference scheme.
On the Convergence of Multi-Grid Methods for a Hypersingular Integral Equation of the First Kind.
On the Convergence of the Classical Jacobi Method for Real Symmetric Matrices with Non-Distinct Eigenvalues.