The approximate cardinal basis function (ACBF) preconditioning technique has been used to solve partial differential equations (PDEs) with radial basis functions (RBFs). In [31], a preconditioning scheme that is based upon constructing the least-squares approximate cardinal basis function from linear combinations of the RBF-PDE matrix elements has shown very attractive numerical results. This p...

This paper suggests a cognitive basis for the isomorphism of a utility function and a distribution function. With only a minimal set of cognitive tools ordinal comparison and frequency processing an object can be evaluated by its relative position in a reference set. This cognitive evaluation, coupled with “more is better” preferences, is consistent with possession of a cardinal utility functio...

An efficient class of nonlinear models, constructed using cardinal B-spline (CBS) basis functions, are proposed for high tide forecasts at the Venice lagoon. Accurate short term predictions of high tides in the lagoon can easily be calculated using the proposed CBS models.

We propose several approaches to the numerical solution of a new Fredholm integro-differential equations modelling neural networks. A solution strategy based on expansions onto standard cardinal basis functions and collocation is presented. Comparative numerical experiments illustrate specific advantages and drawbacks of the different approaches and are used to motivate alternate strategies. 20...

Suppose is a positive number. Basic theory of cardinal interpolation ensures the existence of the Gaussian cardinal function L (x) = P k2Z c k exp(?(x ? k) 2), x 2 R, satisfying the interpolatory conditions L (j) = 0j , j 2 Z. The paper considers the Gaussian cardinal interpolation operator as a linear mapping from`p (Z) into L p (R), 1 p < 1, and in particular, its behaviour as ! 0 +. It is sh...