and infinitely many integers n, multiplication in a normal basis of Fqn over Fq can be computed with O(n logn loglogn), division with O(n log n loglogn) operations in Fq , and exponentiation of an arbitrary element in Fqn with O(n2 loglogn) operations in Fq . We also prove that using a polynomial basis exponentiation in F2n can be done with the same number of operations in F2 for all n. The pre...

This paper compares radial basis function interpolants on diier-ent spaces. The spaces are generated by other radial basis functions, and comparison is done via an explicit representation of the norm of the error functional. The results pose some new questions for further research.

A radial basis function (RBF) has the general form

Monitoring nitrogen concentration of oilseed rape from hyperspectral data using radial basis function Fumin Wang, Jingfeng Huang, Yuan Wang, Zhuanyu Liu, Dailiang Peng & Feifeng Cao a Institute of Hydrology and Water Resources, Zhejiang University, Hangzhou, China b Institute of Agricultural Remote Sensing & Information Application, Zhejiang University, Hangzhou, China c Institute of Remote Sen...

Clinical neurology has been traditionally considered as an academic speciality in which the specialist regurgitates his/her knowledge of neurology without being able to do much for the patient. This attitude is no longer acceptable. Surge of information and discoveries in neurosciences within the last two decades translated into therapeutic interventions which is literally life saving in some o...

Radial basis function networks (RBF) are efficient general function approximators. They show good generalization performance and they are easy to train. Due to theoretical considerations RBFs commonly use Gaussian activation functions. It has been shown that these tight restrictions on the choice of possible activation functions can be relaxed in practical applications. As an alternative differ...

Our goal is to create a natural Italian talking face with, in particular, lip-readable movements. Based on real data extracted from an Italian speaker with the ELITE system, we have approximated the data using radial basis functions. In this paper we present our 3D facial model based on MPEG-4 standard and our computational model of lip movements for Italian. Our experiment is based on some pho...

The complexity of the dual basis of a type I optimal normal basis of Fqn over Fq was determined to be 3n − 3 or 3n − 2 according as q is even or odd, respectively, by Z.-X. Wan and K. Zhou in 2007. We give a new proof to this result by clearly deriving the dual of a type I optimal basis with the aid of a lemma on the dual of a polynomial basis.

This paper presents a new approach for the Radial Basis Function (RBF) interpolation of a vector field. Standard approaches for interpolation randomly select points for interpolation. Our approach uses the knowledge of vector field topology and selects points for interpolation according to the critical points location. We presents the results of interpolation errors on a vector field generated ...