On the row sum condition and the convergence of iteration processes (Preliminary communication)
On the Schwarz algorithms for the elliptic exterior boundary value problems
Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical convergence...
On the Schwarz algorithms for the Elliptic Exterior Boundary Value Problems
Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical convergence...
On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes
Cell-centered and vertex-centered finite volume schemes for the Laplace equation with homogeneous Dirichlet boundary conditions are considered on a triangular mesh and on the Voronoi diagram associated to its vertices. A broken P1 function is constructed from the solutions of both schemes. When the domain is two-dimensional polygonal convex, it is shown that this reconstruction converges with second-order accuracy towards the exact solution in the L2 norm, under the sufficient condition that the...
On the second-order convergence of a function reconstructed from finite volume approximations of the Laplace equation on Delaunay-Voronoi meshes
Cell-centered and vertex-centered finite volume schemes for the Laplace equation with homogeneous Dirichlet boundary conditions are considered on a triangular mesh and on the Voronoi diagram associated to its vertices. A broken P1 function is constructed from the solutions of both schemes. When the domain is two-dimensional polygonal convex, it is shown that this reconstruction converges with second-order accuracy towards the exact solution in the L2 norm, under the sufficient condition that the...
On the semilocal convergence of a fast two-step Newton method.
On the semilocal convergence of a two-step Newton-like projection method for ill-posed equations
We present new semilocal convergence conditions for a two-step Newton-like projection method of Lavrentiev regularization for solving ill-posed equations in a Hilbert space setting. The new convergence conditions are weaker than in earlier studies. Examples are presented to show that older convergence conditions are not satisfied but the new conditions are satisfied.
On the Sensitivity of Orthogonal Polynomials to Perturbations in the Moments.
On the set of weighted least squares solutions of systems of convex inequalities
On the sharpness of a superconvergence estimate in connection with one-dimensional Galerkin-methods.
On the Sharpness of Some Upper Bounds for the Spectral Radii of S.O.R. Iteration Matrices.
On the Sharpness of Theorems Concerning Zero-Free Regions for Certain Sequences of Polynomials.
On the shifted QR iteration applied to companion matrices.
On the singular decomposition of matrices.
On the singular two-parameter eigenvalue problem.
On the singular values and eigenvalues of the Fox-Li and related operators.
On the smoothing spline regression models.
On the solution and applications of generalized equations using Newton's method
We provide local and semilocal convergence results for Newton's method when used to solve generalized equations. Using Lipschitz as well as center-Lipschitz conditions on the operators involved instead of just Lipschitz conditions we show that our Newton-Kantorovich hypotheses are weaker than earlier sufficient conditions for the convergence of Newton's method. In the semilocal case we provide finer error bounds and a better information on the location of the solution. In the local case we can provide...
On the solution of a class of equations with monotone operators by iteration and projection-iteration
On the solution of a differential equation occurring in the problem of heat convection in laminar flow through a tube with slip-flow.