The main computational steps in algebraic softdecoding, as well as Sudan-type list-decoding, of Reed-Solomon codes are bivariate polynomial interpolation and factorization. We introduce a computational technique, based upon re-encoding and coordinate transformation, that significantly reduces the complexity of the bivariate interpolation procedure. This re-encoding and coordinate transformation...

Under certain assumptions on the compactly supported function 2 C(R d), we propose two methods of selecting a function s from the scaled principal shift-invariant space S h () such that s interpolates a given function f at a scattered set of data locations. For both methods, the selection scheme amounts to solving a quadratic programming problem and we are able to prove errror estimates similar...

An m x n matrix E with n ones and (m — l)/i zeros, which satisfies the Polya condition, may be regular and singular for Birkhoff interpolation. We prove that for random distributed ones, E is singular with probability that converges to one if m, n -» oo. Previously, this was known only if m > (1 + 8)n/log n. For constant m and n -» oo, the probability is asymptotically at least i.

A new method to refine the event region in a gridbased WSN is presented. The proposed method determines the fine-grained event region from its coarse-grained version using repeated spatial interpolation. Keywords—Coarse-grained event region, fine-grained event region, inverse distance weighting, spatial interpolation, wireless sensor network,

An interpolation problem of Nevanlinna-Pick type for complexvalued Schur functions in the open unit disk is considered. We prescribe the values of the function and its derivatives up to a certain order at finitely many points. Primarily, we study the case that there exist many Schur functions fulfilling the required conditions. For this situation, an application of the theory of orthogonal rati...

We obtain necessary and sufficient conditions for NevanlinnaPick interpolation on the unit disk with the additional restriction that all analytic interpolating functions satisfy f ′(0) = 0. Alternatively, these results can be interpreted as interpolation results for H∞(V ), where V is the intersection of the bidisk with an algebraic variety. We use an analysis of C*-envelopes to show that these...

In this paper we discuss the problem of numerically computing Petersson inner products of modular forms, given their q-expansion at∞. A formula of Nelson [Nel15] reduces this to obtaining q-expansions at all cusps, and we describe two algorithms based on linear interpolation for numerically obtaining such expansions. We apply our methods to numerically verify constants arising in an explicit ve...

In this paper we present a novel interpolation technique for Vlasov simulations of intense space charge dominated beams. This new technique enables to localize the cubic spline interpolation generally performed in semi-Lagrangian Vlasov codes and thus to improve the scalability of the parallel version. This new method is applied to the propagation of a potassium beam in a periodic focusing chan...