Monotonicity properties of the relative error of a Padé approximation for Mills' ratio.
Monotonicity results for a compound quadrature method for finite-part integrals.
Monotony in Interpolatory Quadratures.
More examples on general order multivariate Padé approximants for pseudo-multivariate functions.
Multilevel Decompositions of Functional Spaces.
Multiple Zeros and Applications to Optimal Linear Functionals.
Multiple-Precision Correctly rounded Newton-Cotes quadrature
Numerical integration is an important operation for scientific computations. Although the different quadrature methods have been well studied from a mathematical point of view, the analysis of the actual error when performing the quadrature on a computer is often neglected. This step is however required for certified arithmetics. We study the Newton-Cotes quadrature scheme in the context of multiple-precision arithmetic and give enough details on the algorithms and the error bounds to enable software...
Multivariate approximation theory with -splines
Multivariate asymptotics for products of large powers with applications to Lagrange inversion.
Multivariate Birkhoff-Lagrange interpolation schemes and Cartesian sets of nodes.
Multivariate interpolation II of Langrange and Hermite type
Multivariate Padé Approximation.
Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods
We give a state-of-the-art survey of investigations concerning multivariate polynomial inequalities. A satisfactory theory of such inequalities has been developed due to applications of both the Gabrielov-Hironaka-Łojasiewicz subanalytic geometry and pluripotential methods based on the complex Monge-Ampère operator. Such an approach permits one to study various inequalities for polynomials restricted not only to nice (nonpluripolar) compact subsets of ℝⁿ or ℂⁿ but also their versions for pieces...
Multivariate smooth interpolation that employs polyharmonic functions
We study the problem of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines complemented with lower order polynomial terms. In general, such formulae can be very useful e.g. in geographic information systems or computer aided geometric design. A simple computational example...
Multivariate spline functions, B-spline bases and polynomial interpolations II
Müntz type theorems. I.
-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.
Nachtrag zu G. Leha: Relative Korovkin-Sätze und Ränder.
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.