-widths for singularly perturbed problems
-widths for singularly perturbed problems
Kolmogorov -widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the -widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.
Natural and smoothing quadratic spline. (An elementary approach)
For quadratic spine interpolating local integrals (mean-values) on a given mesh the conditions of existence and uniqueness, construction under various boundary conditions and other properties are studied. The extremal property of such's spline allows us to present an elementary construction and an algorithm for computing needed parameters of such quadratic spline smoothing given mean-values. Examples are given illustrating the results.
Natural Continuous Extensions of Runge-Kutta Methods for Volterra Integrodifferential Equations.
Natural Runge-Kutta and Projection Methods.
Natural Spline Functions, Their Associated Eigenvalue Problem.
Navier-Stokes/Darcy coupling: modeling, analysis, and numerical approximation.
Near-best approximations to the solution of Fredholm integral equation of the second kind
Near-exact distributions for the generalized Wilks Lambda statistic
Two near-exact distributions for the generalized Wilks Lambda statistic, used to test the independence of several sets of variables with a multivariate normal distribution, are developed for the case where two or more of these sets have an odd number of variables. Using the concept of near-exact distribution and based on a factorization of the exact characteristic function we obtain two approximations, which are very close to the exact distribution but far more manageable. These near-exact distributions...
Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing
We analyze a general multigrid method with aggressive coarsening and polynomial smoothing. We use a special polynomial smoother that originates in the context of the smoothed aggregation method. Assuming the degree of the smoothing polynomial is, on each level , at least , we prove a convergence result independent of . The suggested smoother is cheaper than the overlapping Schwarz method that allows to prove the same result. Moreover, unlike in the case of the overlapping Schwarz method, analysis...
Necessary and sufficient conditions for hypoelliptic of certain left invariant operators on nilpotent Lie groups II.
Necessary and sufficient conditions for the convergence of approximate Picard's iterates for nonlinear boundary value problems
Necessary conditions for the convergence of the generalized periodic overimplicit multistep method
This paper is the continuation of the paper "Generalized periodic overimplicit multistep methods" of the same author and it deals with the necessary and, in some special cases, with the necessary and sufficient conditions for the convergence of general periodic overimplicit multistep methods.
Necessary conditions for the multiple integral problem and elliptic variational inequalities
Necessary conditions for uniform convergence of finite difference schemes for convection-diffusion problems with exponential and parabolic layers
Singularly perturbed problems of convection-diffusion type cannot be solved numerically in a completely satisfactory manner by standard numerical methods. This indicates the need for robust or -uniform methods. In this paper we derive new conditions for such schemes with special emphasize to parabolic layers.
Některé metody pro určení numerické hodnoty funkce
Nested Bounds for the Spectral Radius.
Nested sequences of Chebyshev spaces and shape parameters
Neumann-Neumann algorithms for spectral elements in three dimensions
Neumann-Neumann methods for vector field problems.