We introduce a class of matrix-valued radial basis functions (RBFs) of compact support that can be customized, e.g. chosen to be divergence-free. We then derive and discuss error estimates for interpolants and derivatives based on these matrixvalued RBFs.

The essence of Stahl-Gonchar-Rakhmanov theory of symmetric contours as applied to the multipoint Padé approximants is the fact that given a germ of an algebraic function and a sequence of rational interpolants with free poles of the germ, if there exists a contour that is “symmetric” with respect to the interpolation scheme, does not separate the plane, and in the complement of which the germ h...

Golomb and Weinberger [1] described a variational approach to interpolation which reduced the problem to minimizing a norm in a reproducing kernel Hilbert space generated by means of a small number of data points. Later, Duchon [2] defined radial basis function interpolants as functions which minimize a suitable seminorm given by a weight in spaces of distributions closely related to Sobolev sp...

Divergence-free vector field interpolants properties are explored on uniform and scattered nodes, and also their application to fluid flow problems. These interpolants may be applied to physical problems that require the approximant to have zero divergence, such as the velocity field in the incompressible Navier-Stokes equations and the magnetic and electric fields in the Maxwell’s equations. I...

Terminologies used in life sciences, health-care, and other knowledge intensive areas are often very large and comprehensive. Examples are the medical terminology SNOMED CT (Systematised Nomenclature of Medicine Clinical Terms) [17] containing about 380 000 concept definitions and the National Cancer Institute ontology (NCI) [16] containing more than 60 000 axioms. For terminologies T of this s...

We develop foundations for computing Craig-Lyndon interpolants of two given formulas with first-order theorem provers that construct clausal tableaux. Provers can be understood in this way include efficient machine-oriented systems based on calculi families: goal-oriented such as model elimination and the connection method, bottom-up hypertableau calculus. present first interpolation method pro...

Abstract We consider here the problem of constructing a general recursive algorithm to interpolate given set data with rational function. While many algorithms this kind already exist, they are either providing non-minimal degree solutions (like Schur algorithm) or exhibit jumps in interpolants (or partial realization, as is called when interpolation at infinity, see Rissanen (SIAM J Control 9(...