Lagrange interpolation is a classical method for approximating a continuous function by a polynomial that agrees with the function at a number of chosen points (the “nodes”). However, the accuracy of the approximation is greatly influenced by the location of these nodes. Now, a useful way to measure a given set of nodes to determine whether its Lagrange polynomials are likely to provide good ap...

We introduce an efficient interpolation attack which gives the tighter upper bound of the complexity and the number of pairs of plaintexts and ciphertexts required for the attack. In the previously known interpolation attack there is a problem in that the required complexity for the attack can be overestimated. We solve this problem by first, finding the actual number of coefficients in the pol...

Pilot Symbol Assisted Modulation (PSAM) channel estimation techniques over Rayleigh fading channels have been analysed in recent years. Fluctuations in the Rayleigh fading channel gain degrades the performance of any modulation scheme. This paper develops and analyses a PSAM Polynomial interpolation technique based on Least Square (LS ) approximations to estimate the Channel State Information (...

In this paper, the Bagley-Torvik equation is constructed. A model approach based on non-polynomial numerical methods spline interpolation is developed to solve some problems. We show that the approximate solutions of such problems obtained by the numerical algorithm developed using non-polynomial spline interpolation functions are better than those produced by other numerical methods. The aim o...

The interpolation step of Wu list decoding algorithm for Reed-Solomon codes is considered. The problem is reformulated as construction of a partially homogenized interpolation polynomial. A generalization of the binary interpolation algorithm, which is based on the novel formulation of the interpolation step, is provided. It enables complexity reducion both with respect to the Wu method based o...

In this paper we develop a polynomial spline approximation for data in Euclidean space. The approach considered involves generating an abstract set which provides a unique parametrization of the geometry of the data considered. Polynomial functions from this set to Euclidean space are considered which provide an interpolation function whose computational cost grows at worst iineruly with the di...

A formula for the error in Chung-Yao interpolation announced earlier is proved (by induction). In the process, a bivariate divided difference identity of independent interest is proved. Also, an inductive proof of an error formula for polynomial interpolation by tensorproducts is given. The main tool is a (convenient notation for a) multivariate divided difference. In [2], a particular multivar...