In this paper, we study the minimally supported interpolating filters with prescribed zeros and their corresponding refinable functions.

abstract to estimate spatial variability of soil hydraulic functions, scaling methods were developed and have been widely used. among these functions, physically based methods have been found more desirable because of possibility of estimating soil hydraulic functions from soil physical properties. in this paper, a new and physically based method has been described for scaling soil hydraulic co...

The Dirichlet space D consists of all analytic functions f defined on the unit disk with ∫ |f (z)|dA < ∞. The space of multipliersMD consists of analytic functions φ with φf ∈ D for all f ∈ D. A sequence {zn} ⊂ is called an interpolating sequence for MD if for each bounded sequence of complex numbers {wn} there exists φ ∈ MD with φ(zn) = wn for all n. Our main result is a geometric characteriza...

We estimate the complexity of a general problem for interpolating real algebraic functions given by a black box for their evaluations, extending the results of [GKS 90b, GKS 91b] on interpolation of sparse rational functions.

Gaussian processes~(Kriging) are interpolating data-driven models that frequently applied in various disciplines. Often, processes trained on datasets and subsequently embedded as surrogate optimization problems. These problems nonconvex global is desired. However, previous literature observed computational burdens limiting deterministic to few data points. We propose a reduced-space formulatio...

We consider simultaneous approximation of Nikishin systems of functions by means of rational vector functions which are constructed interpolating along a prescribed table of points. We give sufficient conditions for the uniform convergence of such approximants with a geometric rate.

the accuracy and efficiency of the elements proposed by finite element method (fem) considerably depend on the interpolating functions namely shape functions used to formulate the displacement field within the element. in the present study, novel functions, namely basic displacements functions (bdfs), are introduced and exploited for structural analysis of nanobeams using finite element method ...

We consider the problem of efficiently interpolating an “approximate” black-box polynomial p(x) that is sparse when represented in the Chebyshev basis. Our computations will be in a traditional floating-point environment, and their numerical sensitivity will be investigated. We also consider the related problem of interpolating a sparse linear combination of “approximate” trigonometric function...