This thesis deals with generalized inverses, multivariate polynomial interpolation and approximation of scattered data. Moreover, it covers the lifting scheme, which basically links the aforementioned topics. For instance, determining filters for the lifting scheme is connected to multivariate polynomial interpolation. More precisely, sets of interpolation sites are required that can be interpo...

Abstract—This paper proposes a simple and efficient algorithm using polynomial interpolation for SISO and MIMO-OFDM systems in a fast time-varying channel. The time averages of the multipath complex gains, over the effective duration of each OFDM symbol, are estimated using LS criterion. After that, the time variation of the channel within several OFDM symbols are obtained by interpolating the ...

A new interpolation-based decoding principle for interleaved Gabidulin codes is presented. The approach consists of two steps: First, a multi-variate linearized polynomial is constructed which interpolates the coefficients of the received word and second, the roots of this polynomial have to be found. Due to the specific structure of the interpolation polynomial, both steps (interpolation and r...

Motivated by the development of non-intrusive interpolation methods for parametric PDE’s in high dimension, we have introduced in [8] a sparse multi-variate polynomial interpolation procedure based on the Smolyak formula. The evaluation points lie in an infinite grid ⊗j=0Z where Z = (zj)j≥0 is any infinite sequence of mutually distinct points in some compact X in R or C. A key aspect of the int...

Interpolation by various types of splines is the standard procedure in many applications. In this paper we shall discuss harmonic spline “interpolation” (on the lines of a grid) as an alternative to polynomial spline interpolation (at vertices of a grid). We will discuss some advantages and drawbacks of this approach and present the asymptotics of the Lp-error for adaptive approximation by harm...

We propose a method, which treats metal artifact reduction in CT by sinogram restoration as a problem of scattered data interpolation. Corrupted sinogram entries are discarded and replaced with artificially generated values. The presented interpolation algorithm is based on the 2D non-equispaced fast Fourier transform (NFFT). Results are compared to two common polynomial interpolation schemes.

This paper is concerned with the spline interpolation of functions with a boundary layer component. It is shown that polynomial formulas of spline interpolation for such functions lead to significant errors. We proposed nonpolynomial spline interpolation formulas, fitted to a boundary layer component. Nonsmooth and smooth on whole interval interpolants are constructed. The accuracy of construct...

A new method for determining knots in parametric curve interpolation is presented. The determined knots have a quadratic polynomial precision in the sense that an interpolation scheme which reproduces quadratic polynomials would reproduce parametric quadratic polynomials if the new method is used to determine knots in the interpolation process. Testing results on the efficiency of the new metho...

The Newton-Lagrange interpolation is a well-known problem in elementary calculus. Recall basic facts concerning this problem [6], [2]. Let Ak, k = 0, 1, 2, . . . and ak, k = 0, 1, 2, . . . be two arbitrary sequences of complex numbers (we assume that all ak are distinct ak 6= aj if k 6= j. By interpolation polynomial we mean a n-degree polynomial Pn(z) whose values at points a0, a1, . . . , an ...