The problems of polynomial interpolation with several variables present more difficulties than those one-dimensional interpolation. first problem is to study the regularity schemes. In fact, it well-known that, in contrast univariate case, there no universal space polynomials which admits unique Lagrange for all point sets a given cardinality, and so will depend on set <math xmlns="http://www.w...

In this work, we investigate a model-order reduction scheme for polynomial systems. We begin with defining the generalized multivariate transfer functions system. Based on this, aim at constructing reduced-order system, interpolating defined given set of interpolation points. Furthermore, provide method, inspired by Loewner approach linear and (quadratic-)bilinear systems, to determine good-qua...

Abstract It is well known that the interpolation error for $$\left| x\right| ^{\alpha },\alpha &gt;0$$ x ? , &gt; 0 in $$L_{\infty }\left[ -1,1\right] $$ <m...

The map H → H↓ assigns to each finite-dimensional space of smooth functions a homogeneous polynomial space of the same dimension. We discuss applications of this map in the areas of multivariate polynomial interpolation, box spline theory and polynomial ideals. §