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.
On the Convergence of the Conjugate Gradient Method for Singular Capacitance Matrix Equations from the Neumann Problem of the Poisson Equation.
On the Convergence of the Symmetric SOR Method for Matrices with Red-Black Ordering.
On the convergence rate of the conjugate gradients in presence of rounding errors.
On the convergence theory of double -weak splittings of type II
Recently, Wang (2017) has introduced the -nonnegative double splitting using the notion of matrices that leave a cone invariant and studied its convergence theory by generalizing the corresponding results for the nonnegative double splitting by Song and Song (2011). However, the convergence theory for -weak regular and -nonnegative double splittings of type II is not yet studied. In this article, we first introduce this class of splittings and then discuss the convergence theory for these sub-classes...
On the Distribution of Errors in the Iterative Solution of a System of Linear Equations. II..
On the Eigenvalue Distribution of a Class of Preconditioning Methods.
On the global and cubic convergence of a quasi-cyclic Jacobi method.
On the local convergence of Kung-Traub's two-point method and its dynamics
In this paper, the local convergence analysis of the family of Kung-Traub's two-point method and the convergence ball for this family are obtained and the dynamical behavior on quadratic and cubic polynomials of the resulting family is studied. We use complex dynamic tools to analyze their stability and show that the region of stable members of this family is vast. Numerical examples are also presented in this study. This method is compared with several widely used solution methods by solving test...
On the Monotonity of Incomplete Factorization.
On the Multigrid Solution of Finite Element Equations With Isoparametric Elements.