Vector Fitting is an effective technique for rational approximation of LTI systems. It has been extended to fit the magnitude of the transfer function in absence of phase data. In this paper, magnitude Vector Fitting is modified to work on inequalities which the magnitude of the transfer function has to satisfy, instead of least squares approximation. The new interval version of the magnitude V...

learning theory, noise, non-linear filters An Occam approximation is an algorithm that takes as input a set of samples of a function and a tolerance e, and produces as output a compact representation of a function that is within e of the given samples. We show that the existence of an Occam approximation is sufficient to guarantee the probably approximate learnability of classes of functions on...

Copper films (250 nm) deposited on glass substrates, at different substrate temperatures. Their optical properties were measured by ellipsometery (single wavelength of 589.3 nm) and spectrophotometery in the spectral range of 200–2600 nm. Kramers Kronig method was used for the analysis of the reflectivity curves of Cu films to obtain the optical constants of the films, while ellipsometery measu...

Keerthi and Shevade (2007) proposed an efficient algorithm for constructing an approximate LARS solution path for logistic regression as a function of the regularization parameter. In this paper we extend their approach to multinomial regression. We show that a brute-force approach leads to a multivariate approximation problem resulting in an infeasible path tracking algorithm. Instead, we intr...

This paper presents a new adaptive impedance control strategy, based on Function Approximation Technique (FAT) to compensate for unknown non-flat environment shape or time-varying environment location. The target impedance in the force controllable direction is modified by incorporating adaptive compensators and the uncertainties are represented by FAT, allowing the update law to be derived eas...

In recent years, the optimization of truss structures has been considered due to their several applications and their simple structure and rapid analysis. DNA computing algorithm is a non-gradient-based method derived from numerical modeling of DNA-based computing performance by new computers with DNA memory known as molecular computers. DNA computing algorithm works based on collective intelli...

Interpolation with translates of a basis function is a common process in approximation theory. One starts with a single function (the basis function) and a set of interpolation points. The most elementary form of the interpolant then consists of a linear combination of all translates by interpolation points of the basis function. Frequently , low degree polynomials are added to the interpolant....

Error estimates for radial basis function interpolation are usually based on the concept of native Hilbert spaces. We investigate how good the well known L p-error estimates are by giving lower bounds. Furthermore we study the process of best L 1-approximation and provide upper bounds for the approximation orders in this case.

Although most work to date on RBFs relates to scattered data approximation and in general to interpolation theory, there has recently been an increased interest in their use for solving partial differential equations (PDEs). This approach, which approximates the whole solution of the PDE directly using RBFs, is very attractive due to the fact that this is truly a mesh-free technique. Kansa [1] ...

Let F be a continuous real-valued function defined on the unit square [—1,11 x [-1, 1]. When developing the rational product approximation to F, a certain type of discontinuity may arise. We develop a variation of a known technique to overcome this discontinuity so that the approximation can be programmed. Rational product approximations to F have been computed using both the second algorithm o...